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

Direct product G=N×Q with N=C2×C6 and Q=C3×C6
dρLabelID
C63216C6^3216,177

Semidirect products G=N:Q with N=C2×C6 and Q=C3×C6
extensionφ:Q→Aut NdρLabelID
(C2×C6)⋊(C3×C6) = C3×S3×A4φ: C3×C6/C3 → C6 ⊆ Aut C2×C6246(C2xC6):(C3xC6)216,166
(C2×C6)⋊2(C3×C6) = A4×C3×C6φ: C3×C6/C6 → C3 ⊆ Aut C2×C654(C2xC6):2(C3xC6)216,173
(C2×C6)⋊3(C3×C6) = D4×C33φ: C3×C6/C32 → C2 ⊆ Aut C2×C6108(C2xC6):3(C3xC6)216,151
(C2×C6)⋊4(C3×C6) = C32×C3⋊D4φ: C3×C6/C32 → C2 ⊆ Aut C2×C636(C2xC6):4(C3xC6)216,139
(C2×C6)⋊5(C3×C6) = S3×C62φ: C3×C6/C32 → C2 ⊆ Aut C2×C672(C2xC6):5(C3xC6)216,174

Non-split extensions G=N.Q with N=C2×C6 and Q=C3×C6
extensionφ:Q→Aut NdρLabelID
(C2×C6).1(C3×C6) = A4×C18φ: C3×C6/C6 → C3 ⊆ Aut C2×C6543(C2xC6).1(C3xC6)216,103
(C2×C6).2(C3×C6) = C2×C9⋊A4φ: C3×C6/C6 → C3 ⊆ Aut C2×C6543(C2xC6).2(C3xC6)216,104
(C2×C6).3(C3×C6) = C6×C3.A4φ: C3×C6/C6 → C3 ⊆ Aut C2×C654(C2xC6).3(C3xC6)216,105
(C2×C6).4(C3×C6) = C2×C32.A4φ: C3×C6/C6 → C3 ⊆ Aut C2×C6183(C2xC6).4(C3xC6)216,106
(C2×C6).5(C3×C6) = C2×C32⋊A4φ: C3×C6/C6 → C3 ⊆ Aut C2×C6183(C2xC6).5(C3xC6)216,107
(C2×C6).6(C3×C6) = D4×C3×C9φ: C3×C6/C32 → C2 ⊆ Aut C2×C6108(C2xC6).6(C3xC6)216,76
(C2×C6).7(C3×C6) = D4×He3φ: C3×C6/C32 → C2 ⊆ Aut C2×C6366(C2xC6).7(C3xC6)216,77
(C2×C6).8(C3×C6) = D4×3- 1+2φ: C3×C6/C32 → C2 ⊆ Aut C2×C6366(C2xC6).8(C3xC6)216,78
(C2×C6).9(C3×C6) = Dic3×C3×C6φ: C3×C6/C32 → C2 ⊆ Aut C2×C672(C2xC6).9(C3xC6)216,138
(C2×C6).10(C3×C6) = C2×C4×He3central extension (φ=1)72(C2xC6).10(C3xC6)216,74
(C2×C6).11(C3×C6) = C2×C4×3- 1+2central extension (φ=1)72(C2xC6).11(C3xC6)216,75
(C2×C6).12(C3×C6) = C23×He3central extension (φ=1)72(C2xC6).12(C3xC6)216,115
(C2×C6).13(C3×C6) = C23×3- 1+2central extension (φ=1)72(C2xC6).13(C3xC6)216,116

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