# Extensions 1→N→G→Q→1 with N=C12 and Q=C3×C6

Direct product G=N×Q with N=C12 and Q=C3×C6
dρLabelID
C3×C6×C12216C3xC6xC12216,150

Semidirect products G=N:Q with N=C12 and Q=C3×C6
extensionφ:Q→Aut NdρLabelID
C121(C3×C6) = C32×D12φ: C3×C6/C32C2 ⊆ Aut C1272C12:1(C3xC6)216,137
C122(C3×C6) = S3×C3×C12φ: C3×C6/C32C2 ⊆ Aut C1272C12:2(C3xC6)216,136
C123(C3×C6) = D4×C33φ: C3×C6/C32C2 ⊆ Aut C12108C12:3(C3xC6)216,151

Non-split extensions G=N.Q with N=C12 and Q=C3×C6
extensionφ:Q→Aut NdρLabelID
C12.1(C3×C6) = C32×Dic6φ: C3×C6/C32C2 ⊆ Aut C1272C12.1(C3xC6)216,135
C12.2(C3×C6) = C32×C3⋊C8φ: C3×C6/C32C2 ⊆ Aut C1272C12.2(C3xC6)216,82
C12.3(C3×C6) = D4×C3×C9φ: C3×C6/C32C2 ⊆ Aut C12108C12.3(C3xC6)216,76
C12.4(C3×C6) = D4×He3φ: C3×C6/C32C2 ⊆ Aut C12366C12.4(C3xC6)216,77
C12.5(C3×C6) = D4×3- 1+2φ: C3×C6/C32C2 ⊆ Aut C12366C12.5(C3xC6)216,78
C12.6(C3×C6) = Q8×C3×C9φ: C3×C6/C32C2 ⊆ Aut C12216C12.6(C3xC6)216,79
C12.7(C3×C6) = Q8×He3φ: C3×C6/C32C2 ⊆ Aut C12726C12.7(C3xC6)216,80
C12.8(C3×C6) = Q8×3- 1+2φ: C3×C6/C32C2 ⊆ Aut C12726C12.8(C3xC6)216,81
C12.9(C3×C6) = Q8×C33φ: C3×C6/C32C2 ⊆ Aut C12216C12.9(C3xC6)216,152
C12.10(C3×C6) = C8×He3central extension (φ=1)723C12.10(C3xC6)216,19
C12.11(C3×C6) = C8×3- 1+2central extension (φ=1)723C12.11(C3xC6)216,20
C12.12(C3×C6) = C2×C4×He3central extension (φ=1)72C12.12(C3xC6)216,74
C12.13(C3×C6) = C2×C4×3- 1+2central extension (φ=1)72C12.13(C3xC6)216,75

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