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Extensions 1→N→G→Q→1 with N=C4×C3⋊S3 and Q=S3

Direct product G=N×Q with N=C4×C3⋊S3 and Q=S3
dρLabelID
C4×S3×C3⋊S372C4xS3xC3:S3432,670

Semidirect products G=N:Q with N=C4×C3⋊S3 and Q=S3
extensionφ:Q→Out NdρLabelID
(C4×C3⋊S3)⋊1S3 = C12⋊S3⋊S3φ: S3/C1 → S3 ⊆ Out C4×C3⋊S37212+(C4xC3:S3):1S3432,295
(C4×C3⋊S3)⋊2S3 = C12.S32φ: S3/C1 → S3 ⊆ Out C4×C3⋊S37212-(C4xC3:S3):2S3432,299
(C4×C3⋊S3)⋊3S3 = C3⋊S3⋊D12φ: S3/C1 → S3 ⊆ Out C4×C3⋊S33612+(C4xC3:S3):3S3432,301
(C4×C3⋊S3)⋊4S3 = C12.91S32φ: S3/C1 → S3 ⊆ Out C4×C3⋊S3726(C4xC3:S3):4S3432,297
(C4×C3⋊S3)⋊5S3 = C4×C32⋊D6φ: S3/C1 → S3 ⊆ Out C4×C3⋊S3366(C4xC3:S3):5S3432,300
(C4×C3⋊S3)⋊6S3 = (C3×D12)⋊S3φ: S3/C3 → C2 ⊆ Out C4×C3⋊S3144(C4xC3:S3):6S3432,661
(C4×C3⋊S3)⋊7S3 = C12.40S32φ: S3/C3 → C2 ⊆ Out C4×C3⋊S372(C4xC3:S3):7S3432,665
(C4×C3⋊S3)⋊8S3 = C3⋊S3×D12φ: S3/C3 → C2 ⊆ Out C4×C3⋊S372(C4xC3:S3):8S3432,672
(C4×C3⋊S3)⋊9S3 = C12⋊S3⋊12S3φ: S3/C3 → C2 ⊆ Out C4×C3⋊S3484(C4xC3:S3):9S3432,688
(C4×C3⋊S3)⋊10S3 = C12⋊3S32φ: S3/C3 → C2 ⊆ Out C4×C3⋊S3484(C4xC3:S3):10S3432,691
(C4×C3⋊S3)⋊11S3 = C12.73S32φ: S3/C3 → C2 ⊆ Out C4×C3⋊S372(C4xC3:S3):11S3432,667
(C4×C3⋊S3)⋊12S3 = C12.95S32φ: S3/C3 → C2 ⊆ Out C4×C3⋊S3484(C4xC3:S3):12S3432,689
(C4×C3⋊S3)⋊13S3 = C4×C32⋊4D6φ: S3/C3 → C2 ⊆ Out C4×C3⋊S3484(C4xC3:S3):13S3432,690

Non-split extensions G=N.Q with N=C4×C3⋊S3 and Q=S3
extensionφ:Q→Out NdρLabelID
(C4×C3⋊S3).1S3 = C3⋊S3⋊Dic6φ: S3/C1 → S3 ⊆ Out C4×C3⋊S37212-(C4xC3:S3).1S3432,294
(C4×C3⋊S3).2S3 = C32⋊C6⋊C8φ: S3/C1 → S3 ⊆ Out C4×C3⋊S3726(C4xC3:S3).2S3432,76
(C4×C3⋊S3).3S3 = He3⋊M4(2)φ: S3/C1 → S3 ⊆ Out C4×C3⋊S3726(C4xC3:S3).3S3432,77
(C4×C3⋊S3).4S3 = C3⋊S3×Dic6φ: S3/C3 → C2 ⊆ Out C4×C3⋊S3144(C4xC3:S3).4S3432,663
(C4×C3⋊S3).5S3 = C3⋊S3⋊4Dic6φ: S3/C3 → C2 ⊆ Out C4×C3⋊S3484(C4xC3:S3).5S3432,687
(C4×C3⋊S3).6S3 = C33⋊8M4(2)φ: S3/C3 → C2 ⊆ Out C4×C3⋊S3144(C4xC3:S3).6S3432,434
(C4×C3⋊S3).7S3 = C12.93S32φ: S3/C3 → C2 ⊆ Out C4×C3⋊S3484(C4xC3:S3).7S3432,455
(C4×C3⋊S3).8S3 = C33⋊10M4(2)φ: S3/C3 → C2 ⊆ Out C4×C3⋊S3484(C4xC3:S3).8S3432,456
(C4×C3⋊S3).9S3 = C33⋊7(C2×C8)φ: S3/C3 → C2 ⊆ Out C4×C3⋊S3484(C4xC3:S3).9S3432,635
(C4×C3⋊S3).10S3 = C33⋊4M4(2)φ: S3/C3 → C2 ⊆ Out C4×C3⋊S3484(C4xC3:S3).10S3432,636
(C4×C3⋊S3).11S3 = C4×C33⋊C4φ: S3/C3 → C2 ⊆ Out C4×C3⋊S3484(C4xC3:S3).11S3432,637
(C4×C3⋊S3).12S3 = C33⋊9(C4⋊C4)φ: S3/C3 → C2 ⊆ Out C4×C3⋊S3484(C4xC3:S3).12S3432,638
(C4×C3⋊S3).13S3 = C3⋊S3×C3⋊C8φ: trivial image144(C4xC3:S3).13S3432,431

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