# Extensions 1→N→G→Q→1 with N=C2×C3⋊S3 and Q=C23

Direct product G=N×Q with N=C2×C3⋊S3 and Q=C23
dρLabelID
C24×C3⋊S3144C2^4xC3:S3288,1044

Semidirect products G=N:Q with N=C2×C3⋊S3 and Q=C23
extensionφ:Q→Out NdρLabelID
(C2×C3⋊S3)⋊1C23 = C2×S3×D12φ: C23/C2C22 ⊆ Out C2×C3⋊S348(C2xC3:S3):1C2^3288,951
(C2×C3⋊S3)⋊2C23 = S32×D4φ: C23/C2C22 ⊆ Out C2×C3⋊S3248+(C2xC3:S3):2C2^3288,958
(C2×C3⋊S3)⋊3C23 = C2×S3×C3⋊D4φ: C23/C2C22 ⊆ Out C2×C3⋊S348(C2xC3:S3):3C2^3288,976
(C2×C3⋊S3)⋊4C23 = C22×C3⋊D12φ: C23/C22C2 ⊆ Out C2×C3⋊S348(C2xC3:S3):4C2^3288,974
(C2×C3⋊S3)⋊5C23 = C2×Dic3⋊D6φ: C23/C22C2 ⊆ Out C2×C3⋊S324(C2xC3:S3):5C2^3288,977
(C2×C3⋊S3)⋊6C23 = C22×C12⋊S3φ: C23/C22C2 ⊆ Out C2×C3⋊S3144(C2xC3:S3):6C2^3288,1005
(C2×C3⋊S3)⋊7C23 = C2×D4×C3⋊S3φ: C23/C22C2 ⊆ Out C2×C3⋊S372(C2xC3:S3):7C2^3288,1007
(C2×C3⋊S3)⋊8C23 = C22×C327D4φ: C23/C22C2 ⊆ Out C2×C3⋊S3144(C2xC3:S3):8C2^3288,1017
(C2×C3⋊S3)⋊9C23 = S32×C23φ: C23/C22C2 ⊆ Out C2×C3⋊S348(C2xC3:S3):9C2^3288,1040

Non-split extensions G=N.Q with N=C2×C3⋊S3 and Q=C23
extensionφ:Q→Out NdρLabelID
(C2×C3⋊S3).1C23 = S32⋊Q8φ: C23/C2C22 ⊆ Out C2×C3⋊S3244(C2xC3:S3).1C2^3288,868
(C2×C3⋊S3).2C23 = C4.4S3≀C2φ: C23/C2C22 ⊆ Out C2×C3⋊S3248+(C2xC3:S3).2C2^3288,869
(C2×C3⋊S3).3C23 = C32⋊C4⋊Q8φ: C23/C2C22 ⊆ Out C2×C3⋊S3488-(C2xC3:S3).3C2^3288,870
(C2×C3⋊S3).4C23 = C4×S3≀C2φ: C23/C2C22 ⊆ Out C2×C3⋊S3244(C2xC3:S3).4C2^3288,877
(C2×C3⋊S3).5C23 = S32⋊D4φ: C23/C2C22 ⊆ Out C2×C3⋊S3244(C2xC3:S3).5C2^3288,878
(C2×C3⋊S3).6C23 = C4⋊S3≀C2φ: C23/C2C22 ⊆ Out C2×C3⋊S3248+(C2xC3:S3).6C2^3288,879
(C2×C3⋊S3).7C23 = C2×S32⋊C4φ: C23/C2C22 ⊆ Out C2×C3⋊S324(C2xC3:S3).7C2^3288,880
(C2×C3⋊S3).8C23 = C62.9D4φ: C23/C2C22 ⊆ Out C2×C3⋊S3244(C2xC3:S3).8C2^3288,881
(C2×C3⋊S3).9C23 = C2×C3⋊S3.Q8φ: C23/C2C22 ⊆ Out C2×C3⋊S348(C2xC3:S3).9C2^3288,882
(C2×C3⋊S3).10C23 = D6≀C2φ: C23/C2C22 ⊆ Out C2×C3⋊S3124+(C2xC3:S3).10C2^3288,889
(C2×C3⋊S3).11C23 = C62⋊D4φ: C23/C2C22 ⊆ Out C2×C3⋊S3248+(C2xC3:S3).11C2^3288,890
(C2×C3⋊S3).12C23 = C4.3PSU3(𝔽2)φ: C23/C2C22 ⊆ Out C2×C3⋊S3488(C2xC3:S3).12C2^3288,891
(C2×C3⋊S3).13C23 = C4×PSU3(𝔽2)φ: C23/C2C22 ⊆ Out C2×C3⋊S3368(C2xC3:S3).13C2^3288,892
(C2×C3⋊S3).14C23 = C4⋊PSU3(𝔽2)φ: C23/C2C22 ⊆ Out C2×C3⋊S3368(C2xC3:S3).14C2^3288,893
(C2×C3⋊S3).15C23 = C2×C2.PSU3(𝔽2)φ: C23/C2C22 ⊆ Out C2×C3⋊S348(C2xC3:S3).15C2^3288,894
(C2×C3⋊S3).16C23 = C62⋊Q8φ: C23/C2C22 ⊆ Out C2×C3⋊S3248+(C2xC3:S3).16C2^3288,895
(C2×C3⋊S3).17C23 = D12.33D6φ: C23/C2C22 ⊆ Out C2×C3⋊S3484(C2xC3:S3).17C2^3288,945
(C2×C3⋊S3).18C23 = C2×D6.6D6φ: C23/C2C22 ⊆ Out C2×C3⋊S348(C2xC3:S3).18C2^3288,949
(C2×C3⋊S3).19C23 = S3×C4○D12φ: C23/C2C22 ⊆ Out C2×C3⋊S3484(C2xC3:S3).19C2^3288,953
(C2×C3⋊S3).20C23 = D1224D6φ: C23/C2C22 ⊆ Out C2×C3⋊S3484(C2xC3:S3).20C2^3288,955
(C2×C3⋊S3).21C23 = D1227D6φ: C23/C2C22 ⊆ Out C2×C3⋊S3244+(C2xC3:S3).21C2^3288,956
(C2×C3⋊S3).22C23 = Dic6.24D6φ: C23/C2C22 ⊆ Out C2×C3⋊S3488-(C2xC3:S3).22C2^3288,957
(C2×C3⋊S3).23C23 = S3×D42S3φ: C23/C2C22 ⊆ Out C2×C3⋊S3488-(C2xC3:S3).23C2^3288,959
(C2×C3⋊S3).24C23 = Dic612D6φ: C23/C2C22 ⊆ Out C2×C3⋊S3248+(C2xC3:S3).24C2^3288,960
(C2×C3⋊S3).25C23 = D1212D6φ: C23/C2C22 ⊆ Out C2×C3⋊S3488-(C2xC3:S3).25C2^3288,961
(C2×C3⋊S3).26C23 = D1213D6φ: C23/C2C22 ⊆ Out C2×C3⋊S3248+(C2xC3:S3).26C2^3288,962
(C2×C3⋊S3).27C23 = Dic6.26D6φ: C23/C2C22 ⊆ Out C2×C3⋊S3488+(C2xC3:S3).27C2^3288,964
(C2×C3⋊S3).28C23 = S3×Q83S3φ: C23/C2C22 ⊆ Out C2×C3⋊S3488+(C2xC3:S3).28C2^3288,966
(C2×C3⋊S3).29C23 = D1216D6φ: C23/C2C22 ⊆ Out C2×C3⋊S3488+(C2xC3:S3).29C2^3288,968
(C2×C3⋊S3).30C23 = C2×D6.3D6φ: C23/C2C22 ⊆ Out C2×C3⋊S348(C2xC3:S3).30C2^3288,970
(C2×C3⋊S3).31C23 = C32⋊2+ 1+4φ: C23/C2C22 ⊆ Out C2×C3⋊S3244(C2xC3:S3).31C2^3288,978
(C2×C3⋊S3).32C23 = C22×S3≀C2φ: C23/C2C22 ⊆ Out C2×C3⋊S324(C2xC3:S3).32C2^3288,1031
(C2×C3⋊S3).33C23 = C22×PSU3(𝔽2)φ: C23/C2C22 ⊆ Out C2×C3⋊S336(C2xC3:S3).33C2^3288,1032
(C2×C3⋊S3).34C23 = C2×C4×C32⋊C4φ: C23/C22C2 ⊆ Out C2×C3⋊S348(C2xC3:S3).34C2^3288,932
(C2×C3⋊S3).35C23 = C2×C4⋊(C32⋊C4)φ: C23/C22C2 ⊆ Out C2×C3⋊S348(C2xC3:S3).35C2^3288,933
(C2×C3⋊S3).36C23 = (C6×C12)⋊5C4φ: C23/C22C2 ⊆ Out C2×C3⋊S3244(C2xC3:S3).36C2^3288,934
(C2×C3⋊S3).37C23 = D4×C32⋊C4φ: C23/C22C2 ⊆ Out C2×C3⋊S3248+(C2xC3:S3).37C2^3288,936
(C2×C3⋊S3).38C23 = Q8×C32⋊C4φ: C23/C22C2 ⊆ Out C2×C3⋊S3488-(C2xC3:S3).38C2^3288,938
(C2×C3⋊S3).39C23 = C2×C62⋊C4φ: C23/C22C2 ⊆ Out C2×C3⋊S324(C2xC3:S3).39C2^3288,941
(C2×C3⋊S3).40C23 = C2×D12⋊S3φ: C23/C22C2 ⊆ Out C2×C3⋊S348(C2xC3:S3).40C2^3288,944
(C2×C3⋊S3).41C23 = C2×Dic3.D6φ: C23/C22C2 ⊆ Out C2×C3⋊S348(C2xC3:S3).41C2^3288,947
(C2×C3⋊S3).42C23 = C2×D6.D6φ: C23/C22C2 ⊆ Out C2×C3⋊S348(C2xC3:S3).42C2^3288,948
(C2×C3⋊S3).43C23 = S32×C2×C4φ: C23/C22C2 ⊆ Out C2×C3⋊S348(C2xC3:S3).43C2^3288,950
(C2×C3⋊S3).44C23 = C2×D6⋊D6φ: C23/C22C2 ⊆ Out C2×C3⋊S348(C2xC3:S3).44C2^3288,952
(C2×C3⋊S3).45C23 = D1223D6φ: C23/C22C2 ⊆ Out C2×C3⋊S3244(C2xC3:S3).45C2^3288,954
(C2×C3⋊S3).46C23 = D12.25D6φ: C23/C22C2 ⊆ Out C2×C3⋊S3488-(C2xC3:S3).46C2^3288,963
(C2×C3⋊S3).47C23 = S32×Q8φ: C23/C22C2 ⊆ Out C2×C3⋊S3488-(C2xC3:S3).47C2^3288,965
(C2×C3⋊S3).48C23 = D1215D6φ: C23/C22C2 ⊆ Out C2×C3⋊S3488-(C2xC3:S3).48C2^3288,967
(C2×C3⋊S3).49C23 = C22×C6.D6φ: C23/C22C2 ⊆ Out C2×C3⋊S348(C2xC3:S3).49C2^3288,972
(C2×C3⋊S3).50C23 = C2×C12.59D6φ: C23/C22C2 ⊆ Out C2×C3⋊S3144(C2xC3:S3).50C2^3288,1006
(C2×C3⋊S3).51C23 = C2×C12.D6φ: C23/C22C2 ⊆ Out C2×C3⋊S3144(C2xC3:S3).51C2^3288,1008
(C2×C3⋊S3).52C23 = C3282+ 1+4φ: C23/C22C2 ⊆ Out C2×C3⋊S372(C2xC3:S3).52C2^3288,1009
(C2×C3⋊S3).53C23 = C2×C12.26D6φ: C23/C22C2 ⊆ Out C2×C3⋊S3144(C2xC3:S3).53C2^3288,1011
(C2×C3⋊S3).54C23 = C3272- 1+4φ: C23/C22C2 ⊆ Out C2×C3⋊S3144(C2xC3:S3).54C2^3288,1012
(C2×C3⋊S3).55C23 = C4○D4×C3⋊S3φ: C23/C22C2 ⊆ Out C2×C3⋊S372(C2xC3:S3).55C2^3288,1013
(C2×C3⋊S3).56C23 = C62.154C23φ: C23/C22C2 ⊆ Out C2×C3⋊S372(C2xC3:S3).56C2^3288,1014
(C2×C3⋊S3).57C23 = C3292- 1+4φ: C23/C22C2 ⊆ Out C2×C3⋊S3144(C2xC3:S3).57C2^3288,1015
(C2×C3⋊S3).58C23 = C23×C32⋊C4φ: C23/C22C2 ⊆ Out C2×C3⋊S348(C2xC3:S3).58C2^3288,1039
(C2×C3⋊S3).59C23 = C22×C4×C3⋊S3φ: trivial image144(C2xC3:S3).59C2^3288,1004
(C2×C3⋊S3).60C23 = C2×Q8×C3⋊S3φ: trivial image144(C2xC3:S3).60C2^3288,1010

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