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Extensions 1→N→G→Q→1 with N=C2×C6 and Q=C3⋊S3

Direct product G=N×Q with N=C2×C6 and Q=C3⋊S3
dρLabelID
C2×C6×C3⋊S372C2xC6xC3:S3216,175

Semidirect products G=N:Q with N=C2×C6 and Q=C3⋊S3
extensionφ:Q→Aut NdρLabelID
(C2×C6)⋊1(C3⋊S3) = C3×C3⋊S4φ: C3⋊S3/C3 → S3 ⊆ Aut C2×C6246(C2xC6):1(C3:S3)216,164
(C2×C6)⋊2(C3⋊S3) = C32⋊4S4φ: C3⋊S3/C3 → S3 ⊆ Aut C2×C636(C2xC6):2(C3:S3)216,165
(C2×C6)⋊3(C3⋊S3) = C3×C32⋊7D4φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C636(C2xC6):3(C3:S3)216,144
(C2×C6)⋊4(C3⋊S3) = C33⋊15D4φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C6108(C2xC6):4(C3:S3)216,149
(C2×C6)⋊5(C3⋊S3) = C22×C33⋊C2φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C6108(C2xC6):5(C3:S3)216,176

Non-split extensions G=N.Q with N=C2×C6 and Q=C3⋊S3
extensionφ:Q→Aut NdρLabelID
(C2×C6).1(C3⋊S3) = C32⋊S4φ: C3⋊S3/C3 → S3 ⊆ Aut C2×C6183(C2xC6).1(C3:S3)216,95
(C2×C6).2(C3⋊S3) = C9⋊S4φ: C3⋊S3/C3 → S3 ⊆ Aut C2×C6366+(C2xC6).2(C3:S3)216,93
(C2×C6).3(C3⋊S3) = C32.3S4φ: C3⋊S3/C3 → S3 ⊆ Aut C2×C654(C2xC6).3(C3:S3)216,94
(C2×C6).4(C3⋊S3) = He3⋊7D4φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C6366(C2xC6).4(C3:S3)216,72
(C2×C6).5(C3⋊S3) = C2×C9⋊Dic3φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C6216(C2xC6).5(C3:S3)216,69
(C2×C6).6(C3⋊S3) = C6.D18φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C6108(C2xC6).6(C3:S3)216,70
(C2×C6).7(C3⋊S3) = C22×C9⋊S3φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C6108(C2xC6).7(C3:S3)216,112
(C2×C6).8(C3⋊S3) = C2×C33⋊5C4φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C6216(C2xC6).8(C3:S3)216,148
(C2×C6).9(C3⋊S3) = C2×He3⋊3C4central extension (φ=1)72(C2xC6).9(C3:S3)216,71
(C2×C6).10(C3⋊S3) = C22×He3⋊C2central extension (φ=1)36(C2xC6).10(C3:S3)216,113
(C2×C6).11(C3⋊S3) = C6×C3⋊Dic3central extension (φ=1)72(C2xC6).11(C3:S3)216,143

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