# Extensions 1→N→G→Q→1 with N=C32×C6 and Q=C23

Direct product G=N×Q with N=C32×C6 and Q=C23
dρLabelID
C2×C63432C2xC6^3432,775

Semidirect products G=N:Q with N=C32×C6 and Q=C23
extensionφ:Q→Aut NdρLabelID
(C32×C6)⋊C23 = C2×S33φ: C23/C1C23 ⊆ Aut C32×C6248+(C3^2xC6):C2^3432,759
(C32×C6)⋊2C23 = S32×C2×C6φ: C23/C2C22 ⊆ Aut C32×C648(C3^2xC6):2C2^3432,767
(C32×C6)⋊3C23 = C22×S3×C3⋊S3φ: C23/C2C22 ⊆ Aut C32×C672(C3^2xC6):3C2^3432,768
(C32×C6)⋊4C23 = C22×C324D6φ: C23/C2C22 ⊆ Aut C32×C648(C3^2xC6):4C2^3432,769
(C32×C6)⋊5C23 = S3×C2×C62φ: C23/C22C2 ⊆ Aut C32×C6144(C3^2xC6):5C2^3432,772
(C32×C6)⋊6C23 = C3⋊S3×C22×C6φ: C23/C22C2 ⊆ Aut C32×C6144(C3^2xC6):6C2^3432,773
(C32×C6)⋊7C23 = C23×C33⋊C2φ: C23/C22C2 ⊆ Aut C32×C6216(C3^2xC6):7C2^3432,774

Non-split extensions G=N.Q with N=C32×C6 and Q=C23
extensionφ:Q→Aut NdρLabelID
(C32×C6).1C23 = S32×Dic3φ: C23/C1C23 ⊆ Aut C32×C6488-(C3^2xC6).1C2^3432,594
(C32×C6).2C23 = S3×C6.D6φ: C23/C1C23 ⊆ Aut C32×C6248+(C3^2xC6).2C2^3432,595
(C32×C6).3C23 = Dic36S32φ: C23/C1C23 ⊆ Aut C32×C6488-(C3^2xC6).3C2^3432,596
(C32×C6).4C23 = S3×D6⋊S3φ: C23/C1C23 ⊆ Aut C32×C6488-(C3^2xC6).4C2^3432,597
(C32×C6).5C23 = S3×C3⋊D12φ: C23/C1C23 ⊆ Aut C32×C6248+(C3^2xC6).5C2^3432,598
(C32×C6).6C23 = D64S32φ: C23/C1C23 ⊆ Aut C32×C6248+(C3^2xC6).6C2^3432,599
(C32×C6).7C23 = D6⋊S32φ: C23/C1C23 ⊆ Aut C32×C6488-(C3^2xC6).7C2^3432,600
(C32×C6).8C23 = (S3×C6)⋊D6φ: C23/C1C23 ⊆ Aut C32×C6248+(C3^2xC6).8C2^3432,601
(C32×C6).9C23 = C3⋊S34D12φ: C23/C1C23 ⊆ Aut C32×C6248+(C3^2xC6).9C2^3432,602
(C32×C6).10C23 = S3×C322Q8φ: C23/C1C23 ⊆ Aut C32×C6488-(C3^2xC6).10C2^3432,603
(C32×C6).11C23 = C335(C2×Q8)φ: C23/C1C23 ⊆ Aut C32×C6488-(C3^2xC6).11C2^3432,604
(C32×C6).12C23 = C336(C2×Q8)φ: C23/C1C23 ⊆ Aut C32×C6248+(C3^2xC6).12C2^3432,605
(C32×C6).13C23 = (S3×C6).D6φ: C23/C1C23 ⊆ Aut C32×C6248+(C3^2xC6).13C2^3432,606
(C32×C6).14C23 = D6.S32φ: C23/C1C23 ⊆ Aut C32×C6488-(C3^2xC6).14C2^3432,607
(C32×C6).15C23 = D6.4S32φ: C23/C1C23 ⊆ Aut C32×C6488-(C3^2xC6).15C2^3432,608
(C32×C6).16C23 = D6.3S32φ: C23/C1C23 ⊆ Aut C32×C6248+(C3^2xC6).16C2^3432,609
(C32×C6).17C23 = D6⋊S3⋊S3φ: C23/C1C23 ⊆ Aut C32×C6488-(C3^2xC6).17C2^3432,610
(C32×C6).18C23 = D6.6S32φ: C23/C1C23 ⊆ Aut C32×C6488-(C3^2xC6).18C2^3432,611
(C32×C6).19C23 = Dic3.S32φ: C23/C1C23 ⊆ Aut C32×C6248+(C3^2xC6).19C2^3432,612
(C32×C6).20C23 = C3×S3×Dic6φ: C23/C2C22 ⊆ Aut C32×C6484(C3^2xC6).20C2^3432,642
(C32×C6).21C23 = C3×D125S3φ: C23/C2C22 ⊆ Aut C32×C6484(C3^2xC6).21C2^3432,643
(C32×C6).22C23 = C3×D12⋊S3φ: C23/C2C22 ⊆ Aut C32×C6484(C3^2xC6).22C2^3432,644
(C32×C6).23C23 = C3×Dic3.D6φ: C23/C2C22 ⊆ Aut C32×C6484(C3^2xC6).23C2^3432,645
(C32×C6).24C23 = C3×D6.D6φ: C23/C2C22 ⊆ Aut C32×C6484(C3^2xC6).24C2^3432,646
(C32×C6).25C23 = C3×D6.6D6φ: C23/C2C22 ⊆ Aut C32×C6484(C3^2xC6).25C2^3432,647
(C32×C6).26C23 = S32×C12φ: C23/C2C22 ⊆ Aut C32×C6484(C3^2xC6).26C2^3432,648
(C32×C6).27C23 = C3×S3×D12φ: C23/C2C22 ⊆ Aut C32×C6484(C3^2xC6).27C2^3432,649
(C32×C6).28C23 = C3×D6⋊D6φ: C23/C2C22 ⊆ Aut C32×C6484(C3^2xC6).28C2^3432,650
(C32×C6).29C23 = S3×C6×Dic3φ: C23/C2C22 ⊆ Aut C32×C648(C3^2xC6).29C2^3432,651
(C32×C6).30C23 = C3×D6.3D6φ: C23/C2C22 ⊆ Aut C32×C6244(C3^2xC6).30C2^3432,652
(C32×C6).31C23 = C3×D6.4D6φ: C23/C2C22 ⊆ Aut C32×C6244(C3^2xC6).31C2^3432,653
(C32×C6).32C23 = C6×C6.D6φ: C23/C2C22 ⊆ Aut C32×C648(C3^2xC6).32C2^3432,654
(C32×C6).33C23 = C6×D6⋊S3φ: C23/C2C22 ⊆ Aut C32×C648(C3^2xC6).33C2^3432,655
(C32×C6).34C23 = C6×C3⋊D12φ: C23/C2C22 ⊆ Aut C32×C648(C3^2xC6).34C2^3432,656
(C32×C6).35C23 = C6×C322Q8φ: C23/C2C22 ⊆ Aut C32×C648(C3^2xC6).35C2^3432,657
(C32×C6).36C23 = C3×S3×C3⋊D4φ: C23/C2C22 ⊆ Aut C32×C6244(C3^2xC6).36C2^3432,658
(C32×C6).37C23 = C3×Dic3⋊D6φ: C23/C2C22 ⊆ Aut C32×C6244(C3^2xC6).37C2^3432,659
(C32×C6).38C23 = S3×C324Q8φ: C23/C2C22 ⊆ Aut C32×C6144(C3^2xC6).38C2^3432,660
(C32×C6).39C23 = (C3×D12)⋊S3φ: C23/C2C22 ⊆ Aut C32×C6144(C3^2xC6).39C2^3432,661
(C32×C6).40C23 = D12⋊(C3⋊S3)φ: C23/C2C22 ⊆ Aut C32×C672(C3^2xC6).40C2^3432,662
(C32×C6).41C23 = C3⋊S3×Dic6φ: C23/C2C22 ⊆ Aut C32×C6144(C3^2xC6).41C2^3432,663
(C32×C6).42C23 = C12.39S32φ: C23/C2C22 ⊆ Aut C32×C672(C3^2xC6).42C2^3432,664
(C32×C6).43C23 = C12.40S32φ: C23/C2C22 ⊆ Aut C32×C672(C3^2xC6).43C2^3432,665
(C32×C6).44C23 = C329(S3×Q8)φ: C23/C2C22 ⊆ Aut C32×C672(C3^2xC6).44C2^3432,666
(C32×C6).45C23 = C12.73S32φ: C23/C2C22 ⊆ Aut C32×C672(C3^2xC6).45C2^3432,667
(C32×C6).46C23 = C12.57S32φ: C23/C2C22 ⊆ Aut C32×C6144(C3^2xC6).46C2^3432,668
(C32×C6).47C23 = C12.58S32φ: C23/C2C22 ⊆ Aut C32×C672(C3^2xC6).47C2^3432,669
(C32×C6).48C23 = C4×S3×C3⋊S3φ: C23/C2C22 ⊆ Aut C32×C672(C3^2xC6).48C2^3432,670
(C32×C6).49C23 = S3×C12⋊S3φ: C23/C2C22 ⊆ Aut C32×C672(C3^2xC6).49C2^3432,671
(C32×C6).50C23 = C3⋊S3×D12φ: C23/C2C22 ⊆ Aut C32×C672(C3^2xC6).50C2^3432,672
(C32×C6).51C23 = C12⋊S32φ: C23/C2C22 ⊆ Aut C32×C672(C3^2xC6).51C2^3432,673
(C32×C6).52C23 = C2×S3×C3⋊Dic3φ: C23/C2C22 ⊆ Aut C32×C6144(C3^2xC6).52C2^3432,674
(C32×C6).53C23 = C62.90D6φ: C23/C2C22 ⊆ Aut C32×C672(C3^2xC6).53C2^3432,675
(C32×C6).54C23 = C62.91D6φ: C23/C2C22 ⊆ Aut C32×C672(C3^2xC6).54C2^3432,676
(C32×C6).55C23 = C2×Dic3×C3⋊S3φ: C23/C2C22 ⊆ Aut C32×C6144(C3^2xC6).55C2^3432,677
(C32×C6).56C23 = C62.93D6φ: C23/C2C22 ⊆ Aut C32×C672(C3^2xC6).56C2^3432,678
(C32×C6).57C23 = C2×C338(C2×C4)φ: C23/C2C22 ⊆ Aut C32×C672(C3^2xC6).57C2^3432,679
(C32×C6).58C23 = C2×C336D4φ: C23/C2C22 ⊆ Aut C32×C6144(C3^2xC6).58C2^3432,680
(C32×C6).59C23 = C2×C337D4φ: C23/C2C22 ⊆ Aut C32×C672(C3^2xC6).59C2^3432,681
(C32×C6).60C23 = C2×C338D4φ: C23/C2C22 ⊆ Aut C32×C672(C3^2xC6).60C2^3432,682
(C32×C6).61C23 = C2×C334Q8φ: C23/C2C22 ⊆ Aut C32×C6144(C3^2xC6).61C2^3432,683
(C32×C6).62C23 = S3×C327D4φ: C23/C2C22 ⊆ Aut C32×C672(C3^2xC6).62C2^3432,684
(C32×C6).63C23 = C3⋊S3×C3⋊D4φ: C23/C2C22 ⊆ Aut C32×C672(C3^2xC6).63C2^3432,685
(C32×C6).64C23 = C6223D6φ: C23/C2C22 ⊆ Aut C32×C636(C3^2xC6).64C2^3432,686
(C32×C6).65C23 = C3⋊S34Dic6φ: C23/C2C22 ⊆ Aut C32×C6484(C3^2xC6).65C2^3432,687
(C32×C6).66C23 = C12⋊S312S3φ: C23/C2C22 ⊆ Aut C32×C6484(C3^2xC6).66C2^3432,688
(C32×C6).67C23 = C12.95S32φ: C23/C2C22 ⊆ Aut C32×C6484(C3^2xC6).67C2^3432,689
(C32×C6).68C23 = C4×C324D6φ: C23/C2C22 ⊆ Aut C32×C6484(C3^2xC6).68C2^3432,690
(C32×C6).69C23 = C123S32φ: C23/C2C22 ⊆ Aut C32×C6484(C3^2xC6).69C2^3432,691
(C32×C6).70C23 = C2×C339(C2×C4)φ: C23/C2C22 ⊆ Aut C32×C648(C3^2xC6).70C2^3432,692
(C32×C6).71C23 = C62.96D6φ: C23/C2C22 ⊆ Aut C32×C6244(C3^2xC6).71C2^3432,693
(C32×C6).72C23 = C2×C339D4φ: C23/C2C22 ⊆ Aut C32×C648(C3^2xC6).72C2^3432,694
(C32×C6).73C23 = C2×C335Q8φ: C23/C2C22 ⊆ Aut C32×C648(C3^2xC6).73C2^3432,695
(C32×C6).74C23 = C6224D6φ: C23/C2C22 ⊆ Aut C32×C6244(C3^2xC6).74C2^3432,696
(C32×C6).75C23 = C3×C6×Dic6φ: C23/C22C2 ⊆ Aut C32×C6144(C3^2xC6).75C2^3432,700
(C32×C6).76C23 = S3×C6×C12φ: C23/C22C2 ⊆ Aut C32×C6144(C3^2xC6).76C2^3432,701
(C32×C6).77C23 = C3×C6×D12φ: C23/C22C2 ⊆ Aut C32×C6144(C3^2xC6).77C2^3432,702
(C32×C6).78C23 = C32×C4○D12φ: C23/C22C2 ⊆ Aut C32×C672(C3^2xC6).78C2^3432,703
(C32×C6).79C23 = S3×D4×C32φ: C23/C22C2 ⊆ Aut C32×C672(C3^2xC6).79C2^3432,704
(C32×C6).80C23 = C32×D42S3φ: C23/C22C2 ⊆ Aut C32×C672(C3^2xC6).80C2^3432,705
(C32×C6).81C23 = S3×Q8×C32φ: C23/C22C2 ⊆ Aut C32×C6144(C3^2xC6).81C2^3432,706
(C32×C6).82C23 = C32×Q83S3φ: C23/C22C2 ⊆ Aut C32×C6144(C3^2xC6).82C2^3432,707
(C32×C6).83C23 = Dic3×C62φ: C23/C22C2 ⊆ Aut C32×C6144(C3^2xC6).83C2^3432,708
(C32×C6).84C23 = C3×C6×C3⋊D4φ: C23/C22C2 ⊆ Aut C32×C672(C3^2xC6).84C2^3432,709
(C32×C6).85C23 = C6×C324Q8φ: C23/C22C2 ⊆ Aut C32×C6144(C3^2xC6).85C2^3432,710
(C32×C6).86C23 = C3⋊S3×C2×C12φ: C23/C22C2 ⊆ Aut C32×C6144(C3^2xC6).86C2^3432,711
(C32×C6).87C23 = C6×C12⋊S3φ: C23/C22C2 ⊆ Aut C32×C6144(C3^2xC6).87C2^3432,712
(C32×C6).88C23 = C3×C12.59D6φ: C23/C22C2 ⊆ Aut C32×C672(C3^2xC6).88C2^3432,713
(C32×C6).89C23 = C3×D4×C3⋊S3φ: C23/C22C2 ⊆ Aut C32×C672(C3^2xC6).89C2^3432,714
(C32×C6).90C23 = C3×C12.D6φ: C23/C22C2 ⊆ Aut C32×C672(C3^2xC6).90C2^3432,715
(C32×C6).91C23 = C3×Q8×C3⋊S3φ: C23/C22C2 ⊆ Aut C32×C6144(C3^2xC6).91C2^3432,716
(C32×C6).92C23 = C3×C12.26D6φ: C23/C22C2 ⊆ Aut C32×C6144(C3^2xC6).92C2^3432,717
(C32×C6).93C23 = C2×C6×C3⋊Dic3φ: C23/C22C2 ⊆ Aut C32×C6144(C3^2xC6).93C2^3432,718
(C32×C6).94C23 = C6×C327D4φ: C23/C22C2 ⊆ Aut C32×C672(C3^2xC6).94C2^3432,719
(C32×C6).95C23 = C2×C338Q8φ: C23/C22C2 ⊆ Aut C32×C6432(C3^2xC6).95C2^3432,720
(C32×C6).96C23 = C2×C4×C33⋊C2φ: C23/C22C2 ⊆ Aut C32×C6216(C3^2xC6).96C2^3432,721
(C32×C6).97C23 = C2×C3312D4φ: C23/C22C2 ⊆ Aut C32×C6216(C3^2xC6).97C2^3432,722
(C32×C6).98C23 = C62.160D6φ: C23/C22C2 ⊆ Aut C32×C6216(C3^2xC6).98C2^3432,723
(C32×C6).99C23 = D4×C33⋊C2φ: C23/C22C2 ⊆ Aut C32×C6108(C3^2xC6).99C2^3432,724
(C32×C6).100C23 = C62.100D6φ: C23/C22C2 ⊆ Aut C32×C6216(C3^2xC6).100C2^3432,725
(C32×C6).101C23 = Q8×C33⋊C2φ: C23/C22C2 ⊆ Aut C32×C6216(C3^2xC6).101C2^3432,726
(C32×C6).102C23 = (Q8×C33)⋊C2φ: C23/C22C2 ⊆ Aut C32×C6216(C3^2xC6).102C2^3432,727
(C32×C6).103C23 = C22×C335C4φ: C23/C22C2 ⊆ Aut C32×C6432(C3^2xC6).103C2^3432,728
(C32×C6).104C23 = C2×C3315D4φ: C23/C22C2 ⊆ Aut C32×C6216(C3^2xC6).104C2^3432,729
(C32×C6).105C23 = D4×C32×C6central extension (φ=1)216(C3^2xC6).105C2^3432,731
(C32×C6).106C23 = Q8×C32×C6central extension (φ=1)432(C3^2xC6).106C2^3432,732
(C32×C6).107C23 = C4○D4×C33central extension (φ=1)216(C3^2xC6).107C2^3432,733

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