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Extensions 1→N→G→Q→1 with N=C22×C3⋊S3 and Q=C22

Direct product G=N×Q with N=C22×C3⋊S3 and Q=C22
dρLabelID
C24×C3⋊S3144C2^4xC3:S3288,1044

Semidirect products G=N:Q with N=C22×C3⋊S3 and Q=C22
extensionφ:Q→Out NdρLabelID
(C22×C3⋊S3)⋊1C22 = D6⋊5D12φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3):1C2^2288,571
(C22×C3⋊S3)⋊2C22 = C62⋊5D4φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3):2C2^2288,625
(C22×C3⋊S3)⋊3C22 = C62⋊12D4φ: C22/C1 → C22 ⊆ Out C22×C3⋊S372(C2^2xC3:S3):3C2^2288,739
(C22×C3⋊S3)⋊4C22 = C62⋊24D4φ: C22/C1 → C22 ⊆ Out C22×C3⋊S372(C2^2xC3:S3):4C2^2288,810
(C22×C3⋊S3)⋊5C22 = C2×S3×D12φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3):5C2^2288,951
(C22×C3⋊S3)⋊6C22 = D12⋊27D6φ: C22/C1 → C22 ⊆ Out C22×C3⋊S3244+(C2^2xC3:S3):6C2^2288,956
(C22×C3⋊S3)⋊7C22 = S32×D4φ: C22/C1 → C22 ⊆ Out C22×C3⋊S3248+(C2^2xC3:S3):7C2^2288,958
(C22×C3⋊S3)⋊8C22 = D12⋊13D6φ: C22/C1 → C22 ⊆ Out C22×C3⋊S3248+(C2^2xC3:S3):8C2^2288,962
(C22×C3⋊S3)⋊9C22 = C2×S3×C3⋊D4φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3):9C2^2288,976
(C22×C3⋊S3)⋊10C22 = C32⋊2+ 1+4φ: C22/C1 → C22 ⊆ Out C22×C3⋊S3244(C2^2xC3:S3):10C2^2288,978
(C22×C3⋊S3)⋊11C22 = C32⋊82+ 1+4φ: C22/C1 → C22 ⊆ Out C22×C3⋊S372(C2^2xC3:S3):11C2^2288,1009
(C22×C3⋊S3)⋊12C22 = C62.154C23φ: C22/C1 → C22 ⊆ Out C22×C3⋊S372(C2^2xC3:S3):12C2^2288,1014
(C22×C3⋊S3)⋊13C22 = C22×C3⋊D12φ: C22/C2 → C2 ⊆ Out C22×C3⋊S348(C2^2xC3:S3):13C2^2288,974
(C22×C3⋊S3)⋊14C22 = C2×Dic3⋊D6φ: C22/C2 → C2 ⊆ Out C22×C3⋊S324(C2^2xC3:S3):14C2^2288,977
(C22×C3⋊S3)⋊15C22 = C22×C12⋊S3φ: C22/C2 → C2 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3):15C2^2288,1005
(C22×C3⋊S3)⋊16C22 = C2×D4×C3⋊S3φ: C22/C2 → C2 ⊆ Out C22×C3⋊S372(C2^2xC3:S3):16C2^2288,1007
(C22×C3⋊S3)⋊17C22 = C22×C32⋊7D4φ: C22/C2 → C2 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3):17C2^2288,1017
(C22×C3⋊S3)⋊18C22 = S32×C23φ: C22/C2 → C2 ⊆ Out C22×C3⋊S348(C2^2xC3:S3):18C2^2288,1040

Non-split extensions G=N.Q with N=C22×C3⋊S3 and Q=C22
extensionφ:Q→Out NdρLabelID
(C22×C3⋊S3).1C22 = C62.D4φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).1C2^2288,385
(C22×C3⋊S3).2C22 = C62.2D4φ: C22/C1 → C22 ⊆ Out C22×C3⋊S3244+(C2^2xC3:S3).2C2^2288,386
(C22×C3⋊S3).3C22 = C62.Q8φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).3C2^2288,395
(C22×C3⋊S3).4C22 = (C6×C12)⋊C4φ: C22/C1 → C22 ⊆ Out C22×C3⋊S3244+(C2^2xC3:S3).4C2^2288,422
(C22×C3⋊S3).5C22 = (C2×C62)⋊C4φ: C22/C1 → C22 ⊆ Out C22×C3⋊S3244(C2^2xC3:S3).5C2^2288,434
(C22×C3⋊S3).6C22 = C62.6C23φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).6C2^2288,484
(C22×C3⋊S3).7C22 = C62.18C23φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).7C2^2288,496
(C22×C3⋊S3).8C22 = C62.20C23φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).8C2^2288,498
(C22×C3⋊S3).9C22 = Dic3.D12φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).9C2^2288,500
(C22×C3⋊S3).10C22 = C62.24C23φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).10C2^2288,502
(C22×C3⋊S3).11C22 = C12.28D12φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).11C2^2288,512
(C22×C3⋊S3).12C22 = C62.38C23φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).12C2^2288,516
(C22×C3⋊S3).13C22 = Dic3⋊4D12φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).13C2^2288,528
(C22×C3⋊S3).14C22 = Dic3⋊D12φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).14C2^2288,534
(C22×C3⋊S3).15C22 = C62.58C23φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).15C2^2288,536
(C22×C3⋊S3).16C22 = D6.D12φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).16C2^2288,538
(C22×C3⋊S3).17C22 = Dic3⋊5D12φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).17C2^2288,542
(C22×C3⋊S3).18C22 = C62.65C23φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).18C2^2288,543
(C22×C3⋊S3).19C22 = C62.67C23φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).19C2^2288,545
(C22×C3⋊S3).20C22 = C62.74C23φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).20C2^2288,552
(C22×C3⋊S3).21C22 = D6⋊D12φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).21C2^2288,554
(C22×C3⋊S3).22C22 = C62.77C23φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).22C2^2288,555
(C22×C3⋊S3).23C22 = C12⋊7D12φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).23C2^2288,557
(C22×C3⋊S3).24C22 = Dic3⋊3D12φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).24C2^2288,558
(C22×C3⋊S3).25C22 = C12⋊D12φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).25C2^2288,559
(C22×C3⋊S3).26C22 = S3×D6⋊C4φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).26C2^2288,568
(C22×C3⋊S3).27C22 = D6⋊4D12φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).27C2^2288,570
(C22×C3⋊S3).28C22 = C62.94C23φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).28C2^2288,600
(C22×C3⋊S3).29C22 = C62.95C23φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).29C2^2288,601
(C22×C3⋊S3).30C22 = C62.100C23φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).30C2^2288,606
(C22×C3⋊S3).31C22 = C62.60D4φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).31C2^2288,614
(C22×C3⋊S3).32C22 = C62.113C23φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).32C2^2288,619
(C22×C3⋊S3).33C22 = C62.117C23φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).33C2^2288,623
(C22×C3⋊S3).34C22 = C62⋊6D4φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).34C2^2288,626
(C22×C3⋊S3).35C22 = C62.121C23φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).35C2^2288,627
(C22×C3⋊S3).36C22 = C62.125C23φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).36C2^2288,631
(C22×C3⋊S3).37C22 = C12⋊4D12φ: C22/C1 → C22 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3).37C2^2288,731
(C22×C3⋊S3).38C22 = C122⋊6C2φ: C22/C1 → C22 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3).38C2^2288,732
(C22×C3⋊S3).39C22 = C122⋊2C2φ: C22/C1 → C22 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3).39C2^2288,733
(C22×C3⋊S3).40C22 = C62.228C23φ: C22/C1 → C22 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3).40C2^2288,741
(C22×C3⋊S3).41C22 = C62.229C23φ: C22/C1 → C22 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3).41C2^2288,742
(C22×C3⋊S3).42C22 = C62.69D4φ: C22/C1 → C22 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3).42C2^2288,743
(C22×C3⋊S3).43C22 = C62.242C23φ: C22/C1 → C22 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3).43C2^2288,755
(C22×C3⋊S3).44C22 = C62.129D4φ: C22/C1 → C22 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3).44C2^2288,786
(C22×C3⋊S3).45C22 = C62⋊19D4φ: C22/C1 → C22 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3).45C2^2288,787
(C22×C3⋊S3).46C22 = C62⋊14D4φ: C22/C1 → C22 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3).46C2^2288,796
(C22×C3⋊S3).47C22 = C62.258C23φ: C22/C1 → C22 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3).47C2^2288,797
(C22×C3⋊S3).48C22 = C62.262C23φ: C22/C1 → C22 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3).48C2^2288,804
(C22×C3⋊S3).49C22 = C2×S32⋊C4φ: C22/C1 → C22 ⊆ Out C22×C3⋊S324(C2^2xC3:S3).49C2^2288,880
(C22×C3⋊S3).50C22 = C62.9D4φ: C22/C1 → C22 ⊆ Out C22×C3⋊S3244(C2^2xC3:S3).50C2^2288,881
(C22×C3⋊S3).51C22 = C2×C3⋊S3.Q8φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).51C2^2288,882
(C22×C3⋊S3).52C22 = D6≀C2φ: C22/C1 → C22 ⊆ Out C22×C3⋊S3124+(C2^2xC3:S3).52C2^2288,889
(C22×C3⋊S3).53C22 = C62⋊D4φ: C22/C1 → C22 ⊆ Out C22×C3⋊S3248+(C2^2xC3:S3).53C2^2288,890
(C22×C3⋊S3).54C22 = C2×C2.PSU3(𝔽2)φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).54C2^2288,894
(C22×C3⋊S3).55C22 = C62⋊Q8φ: C22/C1 → C22 ⊆ Out C22×C3⋊S3248+(C2^2xC3:S3).55C2^2288,895
(C22×C3⋊S3).56C22 = D4×C32⋊C4φ: C22/C1 → C22 ⊆ Out C22×C3⋊S3248+(C2^2xC3:S3).56C2^2288,936
(C22×C3⋊S3).57C22 = C2×D6.6D6φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).57C2^2288,949
(C22×C3⋊S3).58C22 = Dic6⋊12D6φ: C22/C1 → C22 ⊆ Out C22×C3⋊S3248+(C2^2xC3:S3).58C2^2288,960
(C22×C3⋊S3).59C22 = C2×D6.3D6φ: C22/C1 → C22 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).59C2^2288,970
(C22×C3⋊S3).60C22 = C22×S3≀C2φ: C22/C1 → C22 ⊆ Out C22×C3⋊S324(C2^2xC3:S3).60C2^2288,1031
(C22×C3⋊S3).61C22 = C22×PSU3(𝔽2)φ: C22/C1 → C22 ⊆ Out C22×C3⋊S336(C2^2xC3:S3).61C2^2288,1032
(C22×C3⋊S3).62C22 = (C6×C12)⋊2C4φ: C22/C2 → C2 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).62C2^2288,429
(C22×C3⋊S3).63C22 = C62.19C23φ: C22/C2 → C2 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).63C2^2288,497
(C22×C3⋊S3).64C22 = C62.23C23φ: C22/C2 → C2 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).64C2^2288,501
(C22×C3⋊S3).65C22 = C62.35C23φ: C22/C2 → C2 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).65C2^2288,513
(C22×C3⋊S3).66C22 = C12.30D12φ: C22/C2 → C2 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).66C2^2288,519
(C22×C3⋊S3).67C22 = C62.44C23φ: C22/C2 → C2 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).67C2^2288,522
(C22×C3⋊S3).68C22 = C62.51C23φ: C22/C2 → C2 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).68C2^2288,529
(C22×C3⋊S3).69C22 = C4×C6.D6φ: C22/C2 → C2 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).69C2^2288,530
(C22×C3⋊S3).70C22 = C62.53C23φ: C22/C2 → C2 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).70C2^2288,531
(C22×C3⋊S3).71C22 = C62.70C23φ: C22/C2 → C2 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).71C2^2288,548
(C22×C3⋊S3).72C22 = C4×C3⋊D12φ: C22/C2 → C2 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).72C2^2288,551
(C22×C3⋊S3).73C22 = C62.82C23φ: C22/C2 → C2 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).73C2^2288,560
(C22×C3⋊S3).74C22 = C12⋊2D12φ: C22/C2 → C2 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).74C2^2288,564
(C22×C3⋊S3).75C22 = C62.91C23φ: C22/C2 → C2 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).75C2^2288,569
(C22×C3⋊S3).76C22 = C2×C6.D12φ: C22/C2 → C2 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).76C2^2288,611
(C22×C3⋊S3).77C22 = C62.116C23φ: C22/C2 → C2 ⊆ Out C22×C3⋊S324(C2^2xC3:S3).77C2^2288,622
(C22×C3⋊S3).78C22 = C62⋊8D4φ: C22/C2 → C2 ⊆ Out C22×C3⋊S324(C2^2xC3:S3).78C2^2288,629
(C22×C3⋊S3).79C22 = C122⋊16C2φ: C22/C2 → C2 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3).79C2^2288,729
(C22×C3⋊S3).80C22 = C4×C12⋊S3φ: C22/C2 → C2 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3).80C2^2288,730
(C22×C3⋊S3).81C22 = C22⋊C4×C3⋊S3φ: C22/C2 → C2 ⊆ Out C22×C3⋊S372(C2^2xC3:S3).81C2^2288,737
(C22×C3⋊S3).82C22 = C62.225C23φ: C22/C2 → C2 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3).82C2^2288,738
(C22×C3⋊S3).83C22 = C62.227C23φ: C22/C2 → C2 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3).83C2^2288,740
(C22×C3⋊S3).84C22 = C62.236C23φ: C22/C2 → C2 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3).84C2^2288,749
(C22×C3⋊S3).85C22 = C62.237C23φ: C22/C2 → C2 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3).85C2^2288,750
(C22×C3⋊S3).86C22 = C62.238C23φ: C22/C2 → C2 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3).86C2^2288,751
(C22×C3⋊S3).87C22 = C12⋊3D12φ: C22/C2 → C2 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3).87C2^2288,752
(C22×C3⋊S3).88C22 = C62.240C23φ: C22/C2 → C2 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3).88C2^2288,753
(C22×C3⋊S3).89C22 = C12.31D12φ: C22/C2 → C2 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3).89C2^2288,754
(C22×C3⋊S3).90C22 = C2×C6.11D12φ: C22/C2 → C2 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3).90C2^2288,784
(C22×C3⋊S3).91C22 = C4×C32⋊7D4φ: C22/C2 → C2 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3).91C2^2288,785
(C22×C3⋊S3).92C22 = C62⋊13D4φ: C22/C2 → C2 ⊆ Out C22×C3⋊S372(C2^2xC3:S3).92C2^2288,794
(C22×C3⋊S3).93C22 = C62.256C23φ: C22/C2 → C2 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3).93C2^2288,795
(C22×C3⋊S3).94C22 = C62.261C23φ: C22/C2 → C2 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3).94C2^2288,803
(C22×C3⋊S3).95C22 = C2×C4×C32⋊C4φ: C22/C2 → C2 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).95C2^2288,932
(C22×C3⋊S3).96C22 = C2×C4⋊(C32⋊C4)φ: C22/C2 → C2 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).96C2^2288,933
(C22×C3⋊S3).97C22 = (C6×C12)⋊5C4φ: C22/C2 → C2 ⊆ Out C22×C3⋊S3244(C2^2xC3:S3).97C2^2288,934
(C22×C3⋊S3).98C22 = C2×C62⋊C4φ: C22/C2 → C2 ⊆ Out C22×C3⋊S324(C2^2xC3:S3).98C2^2288,941
(C22×C3⋊S3).99C22 = C2×D12⋊S3φ: C22/C2 → C2 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).99C2^2288,944
(C22×C3⋊S3).100C22 = C2×Dic3.D6φ: C22/C2 → C2 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).100C2^2288,947
(C22×C3⋊S3).101C22 = C2×D6.D6φ: C22/C2 → C2 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).101C2^2288,948
(C22×C3⋊S3).102C22 = S32×C2×C4φ: C22/C2 → C2 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).102C2^2288,950
(C22×C3⋊S3).103C22 = C2×D6⋊D6φ: C22/C2 → C2 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).103C2^2288,952
(C22×C3⋊S3).104C22 = D12⋊23D6φ: C22/C2 → C2 ⊆ Out C22×C3⋊S3244(C2^2xC3:S3).104C2^2288,954
(C22×C3⋊S3).105C22 = C22×C6.D6φ: C22/C2 → C2 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).105C2^2288,972
(C22×C3⋊S3).106C22 = C2×C12.59D6φ: C22/C2 → C2 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3).106C2^2288,1006
(C22×C3⋊S3).107C22 = C2×C12.D6φ: C22/C2 → C2 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3).107C2^2288,1008
(C22×C3⋊S3).108C22 = C2×C12.26D6φ: C22/C2 → C2 ⊆ Out C22×C3⋊S3144(C2^2xC3:S3).108C2^2288,1011
(C22×C3⋊S3).109C22 = C4○D4×C3⋊S3φ: C22/C2 → C2 ⊆ Out C22×C3⋊S372(C2^2xC3:S3).109C2^2288,1013
(C22×C3⋊S3).110C22 = C23×C32⋊C4φ: C22/C2 → C2 ⊆ Out C22×C3⋊S348(C2^2xC3:S3).110C2^2288,1039
(C22×C3⋊S3).111C22 = C42×C3⋊S3φ: trivial image144(C2^2xC3:S3).111C2^2288,728
(C22×C3⋊S3).112C22 = C4⋊C4×C3⋊S3φ: trivial image144(C2^2xC3:S3).112C2^2288,748
(C22×C3⋊S3).113C22 = C22×C4×C3⋊S3φ: trivial image144(C2^2xC3:S3).113C2^2288,1004
(C22×C3⋊S3).114C22 = C2×Q8×C3⋊S3φ: trivial image144(C2^2xC3:S3).114C2^2288,1010

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