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Extensions 1→N→G→Q→1 with N=C2×C4⋊C4 and Q=S3

Direct product G=N×Q with N=C2×C4⋊C4 and Q=S3
dρLabelID
C2×S3×C4⋊C496C2xS3xC4:C4192,1060

Semidirect products G=N:Q with N=C2×C4⋊C4 and Q=S3
extensionφ:Q→Out NdρLabelID
(C2×C4⋊C4)⋊1S3 = C2×C6.D8φ: S3/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):1S3192,524
(C2×C4⋊C4)⋊2S3 = C4○D12⋊C4φ: S3/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):2S3192,525
(C2×C4⋊C4)⋊3S3 = (C2×C6).40D8φ: S3/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):3S3192,526
(C2×C4⋊C4)⋊4S3 = C4⋊C4.228D6φ: S3/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):4S3192,527
(C2×C4⋊C4)⋊5S3 = C4⋊(D6⋊C4)φ: S3/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):5S3192,546
(C2×C4⋊C4)⋊6S3 = (C2×D12)⋊10C4φ: S3/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):6S3192,547
(C2×C4⋊C4)⋊7S3 = D6⋊C4⋊6C4φ: S3/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):7S3192,548
(C2×C4⋊C4)⋊8S3 = D6⋊C4⋊7C4φ: S3/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):8S3192,549
(C2×C4⋊C4)⋊9S3 = (C2×C4)⋊3D12φ: S3/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):9S3192,550
(C2×C4⋊C4)⋊10S3 = (C2×C12).289D4φ: S3/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):10S3192,551
(C2×C4⋊C4)⋊11S3 = (C2×C12).290D4φ: S3/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):11S3192,552
(C2×C4⋊C4)⋊12S3 = (C2×C12).56D4φ: S3/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):12S3192,553
(C2×C4⋊C4)⋊13S3 = C6.82+ 1+4φ: S3/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):13S3192,1063
(C2×C4⋊C4)⋊14S3 = C2×D6.D4φ: S3/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):14S3192,1064
(C2×C4⋊C4)⋊15S3 = C2×C12⋊D4φ: S3/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):15S3192,1065
(C2×C4⋊C4)⋊16S3 = C6.2- 1+4φ: S3/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):16S3192,1066
(C2×C4⋊C4)⋊17S3 = C2×D6⋊Q8φ: S3/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):17S3192,1067
(C2×C4⋊C4)⋊18S3 = C2×C4.D12φ: S3/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):18S3192,1068
(C2×C4⋊C4)⋊19S3 = C6.2+ 1+4φ: S3/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):19S3192,1069
(C2×C4⋊C4)⋊20S3 = C6.102+ 1+4φ: S3/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):20S3192,1070
(C2×C4⋊C4)⋊21S3 = C2×C4⋊C4⋊S3φ: S3/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):21S3192,1071
(C2×C4⋊C4)⋊22S3 = C6.52- 1+4φ: S3/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):22S3192,1072
(C2×C4⋊C4)⋊23S3 = C6.112+ 1+4φ: S3/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):23S3192,1073
(C2×C4⋊C4)⋊24S3 = C6.62- 1+4φ: S3/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):24S3192,1074
(C2×C4⋊C4)⋊25S3 = C2×C4⋊C4⋊7S3φ: trivial image96(C2xC4:C4):25S3192,1061
(C2×C4⋊C4)⋊26S3 = C2×Dic3⋊5D4φ: trivial image96(C2xC4:C4):26S3192,1062

Non-split extensions G=N.Q with N=C2×C4⋊C4 and Q=S3
extensionφ:Q→Out NdρLabelID
(C2×C4⋊C4).1S3 = (C2×C12)⋊C8φ: S3/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4).1S3192,87
(C2×C4⋊C4).2S3 = C12.C42φ: S3/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).2S3192,88
(C2×C4⋊C4).3S3 = C12.(C4⋊C4)φ: S3/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4).3S3192,89
(C2×C4⋊C4).4S3 = C2×C6.Q16φ: S3/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).4S3192,521
(C2×C4⋊C4).5S3 = C2×C12.Q8φ: S3/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).5S3192,522
(C2×C4⋊C4).6S3 = C4⋊C4.225D6φ: S3/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4).6S3192,523
(C2×C4⋊C4).7S3 = C2×C6.SD16φ: S3/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).7S3192,528
(C2×C4⋊C4).8S3 = C4⋊C4.230D6φ: S3/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4).8S3192,529
(C2×C4⋊C4).9S3 = C4⋊C4.231D6φ: S3/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4).9S3192,530
(C2×C4⋊C4).10S3 = C12⋊(C4⋊C4)φ: S3/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).10S3192,531
(C2×C4⋊C4).11S3 = C4.(D6⋊C4)φ: S3/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).11S3192,532
(C2×C4⋊C4).12S3 = (C4×Dic3)⋊8C4φ: S3/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).12S3192,534
(C2×C4⋊C4).13S3 = Dic3⋊(C4⋊C4)φ: S3/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).13S3192,535
(C2×C4⋊C4).14S3 = (C4×Dic3)⋊9C4φ: S3/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).14S3192,536
(C2×C4⋊C4).15S3 = C6.67(C4×D4)φ: S3/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).15S3192,537
(C2×C4⋊C4).16S3 = (C2×Dic3)⋊Q8φ: S3/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).16S3192,538
(C2×C4⋊C4).17S3 = C4⋊C4⋊5Dic3φ: S3/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).17S3192,539
(C2×C4⋊C4).18S3 = (C2×C4).44D12φ: S3/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).18S3192,540
(C2×C4⋊C4).19S3 = (C2×C12).54D4φ: S3/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).19S3192,541
(C2×C4⋊C4).20S3 = (C2×Dic3).Q8φ: S3/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).20S3192,542
(C2×C4⋊C4).21S3 = C4⋊C4⋊6Dic3φ: S3/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).21S3192,543
(C2×C4⋊C4).22S3 = (C2×C12).288D4φ: S3/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).22S3192,544
(C2×C4⋊C4).23S3 = (C2×C12).55D4φ: S3/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).23S3192,545
(C2×C4⋊C4).24S3 = C2×C12⋊Q8φ: S3/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).24S3192,1056
(C2×C4⋊C4).25S3 = C2×Dic3.Q8φ: S3/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).25S3192,1057
(C2×C4⋊C4).26S3 = C2×C4.Dic6φ: S3/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).26S3192,1058
(C2×C4⋊C4).27S3 = C6.72+ 1+4φ: S3/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4).27S3192,1059
(C2×C4⋊C4).28S3 = Dic3×C4⋊C4φ: trivial image192(C2xC4:C4).28S3192,533
(C2×C4⋊C4).29S3 = C2×Dic6⋊C4φ: trivial image192(C2xC4:C4).29S3192,1055

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