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Extensions 1→N→G→Q→1 with N=C2×C4 and Q=C3⋊S3

Direct product G=N×Q with N=C2×C4 and Q=C3⋊S3
dρLabelID
C2×C4×C3⋊S372C2xC4xC3:S3144,169

Semidirect products G=N:Q with N=C2×C4 and Q=C3⋊S3
extensionφ:Q→Aut NdρLabelID
(C2×C4)⋊1(C3⋊S3) = C6.11D12φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C472(C2xC4):1(C3:S3)144,95
(C2×C4)⋊2(C3⋊S3) = C2×C12⋊S3φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C472(C2xC4):2(C3:S3)144,170
(C2×C4)⋊3(C3⋊S3) = C12.59D6φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C472(C2xC4):3(C3:S3)144,171

Non-split extensions G=N.Q with N=C2×C4 and Q=C3⋊S3
extensionφ:Q→Aut NdρLabelID
(C2×C4).1(C3⋊S3) = C6.Dic6φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C4144(C2xC4).1(C3:S3)144,93
(C2×C4).2(C3⋊S3) = C12.58D6φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C472(C2xC4).2(C3:S3)144,91
(C2×C4).3(C3⋊S3) = C12⋊Dic3φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C4144(C2xC4).3(C3:S3)144,94
(C2×C4).4(C3⋊S3) = C2×C32⋊4Q8φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C4144(C2xC4).4(C3:S3)144,168
(C2×C4).5(C3⋊S3) = C2×C32⋊4C8central extension (φ=1)144(C2xC4).5(C3:S3)144,90
(C2×C4).6(C3⋊S3) = C4×C3⋊Dic3central extension (φ=1)144(C2xC4).6(C3:S3)144,92

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