# Extensions 1→N→G→Q→1 with N=C12 and Q=C2×C6

Direct product G=N×Q with N=C12 and Q=C2×C6
dρLabelID
C2×C6×C12144C2xC6xC12144,178

Semidirect products G=N:Q with N=C12 and Q=C2×C6
extensionφ:Q→Aut NdρLabelID
C12⋊(C2×C6) = C3×S3×D4φ: C2×C6/C3C22 ⊆ Aut C12244C12:(C2xC6)144,162
C122(C2×C6) = C6×D12φ: C2×C6/C6C2 ⊆ Aut C1248C12:2(C2xC6)144,160
C123(C2×C6) = S3×C2×C12φ: C2×C6/C6C2 ⊆ Aut C1248C12:3(C2xC6)144,159
C124(C2×C6) = D4×C3×C6φ: C2×C6/C6C2 ⊆ Aut C1272C12:4(C2xC6)144,179

Non-split extensions G=N.Q with N=C12 and Q=C2×C6
extensionφ:Q→Aut NdρLabelID
C12.1(C2×C6) = C3×D4⋊S3φ: C2×C6/C3C22 ⊆ Aut C12244C12.1(C2xC6)144,80
C12.2(C2×C6) = C3×D4.S3φ: C2×C6/C3C22 ⊆ Aut C12244C12.2(C2xC6)144,81
C12.3(C2×C6) = C3×Q82S3φ: C2×C6/C3C22 ⊆ Aut C12484C12.3(C2xC6)144,82
C12.4(C2×C6) = C3×C3⋊Q16φ: C2×C6/C3C22 ⊆ Aut C12484C12.4(C2xC6)144,83
C12.5(C2×C6) = C3×D42S3φ: C2×C6/C3C22 ⊆ Aut C12244C12.5(C2xC6)144,163
C12.6(C2×C6) = C3×S3×Q8φ: C2×C6/C3C22 ⊆ Aut C12484C12.6(C2xC6)144,164
C12.7(C2×C6) = C3×Q83S3φ: C2×C6/C3C22 ⊆ Aut C12484C12.7(C2xC6)144,165
C12.8(C2×C6) = C3×C24⋊C2φ: C2×C6/C6C2 ⊆ Aut C12482C12.8(C2xC6)144,71
C12.9(C2×C6) = C3×D24φ: C2×C6/C6C2 ⊆ Aut C12482C12.9(C2xC6)144,72
C12.10(C2×C6) = C3×Dic12φ: C2×C6/C6C2 ⊆ Aut C12482C12.10(C2xC6)144,73
C12.11(C2×C6) = C6×Dic6φ: C2×C6/C6C2 ⊆ Aut C1248C12.11(C2xC6)144,158
C12.12(C2×C6) = C3×C4○D12φ: C2×C6/C6C2 ⊆ Aut C12242C12.12(C2xC6)144,161
C12.13(C2×C6) = S3×C24φ: C2×C6/C6C2 ⊆ Aut C12482C12.13(C2xC6)144,69
C12.14(C2×C6) = C3×C8⋊S3φ: C2×C6/C6C2 ⊆ Aut C12482C12.14(C2xC6)144,70
C12.15(C2×C6) = C6×C3⋊C8φ: C2×C6/C6C2 ⊆ Aut C1248C12.15(C2xC6)144,74
C12.16(C2×C6) = C3×C4.Dic3φ: C2×C6/C6C2 ⊆ Aut C12242C12.16(C2xC6)144,75
C12.17(C2×C6) = C9×D8φ: C2×C6/C6C2 ⊆ Aut C12722C12.17(C2xC6)144,25
C12.18(C2×C6) = C9×SD16φ: C2×C6/C6C2 ⊆ Aut C12722C12.18(C2xC6)144,26
C12.19(C2×C6) = C9×Q16φ: C2×C6/C6C2 ⊆ Aut C121442C12.19(C2xC6)144,27
C12.20(C2×C6) = D4×C18φ: C2×C6/C6C2 ⊆ Aut C1272C12.20(C2xC6)144,48
C12.21(C2×C6) = Q8×C18φ: C2×C6/C6C2 ⊆ Aut C12144C12.21(C2xC6)144,49
C12.22(C2×C6) = C9×C4○D4φ: C2×C6/C6C2 ⊆ Aut C12722C12.22(C2xC6)144,50
C12.23(C2×C6) = C32×D8φ: C2×C6/C6C2 ⊆ Aut C1272C12.23(C2xC6)144,106
C12.24(C2×C6) = C32×SD16φ: C2×C6/C6C2 ⊆ Aut C1272C12.24(C2xC6)144,107
C12.25(C2×C6) = C32×Q16φ: C2×C6/C6C2 ⊆ Aut C12144C12.25(C2xC6)144,108
C12.26(C2×C6) = Q8×C3×C6φ: C2×C6/C6C2 ⊆ Aut C12144C12.26(C2xC6)144,180
C12.27(C2×C6) = C32×C4○D4φ: C2×C6/C6C2 ⊆ Aut C1272C12.27(C2xC6)144,181
C12.28(C2×C6) = C9×M4(2)central extension (φ=1)722C12.28(C2xC6)144,24
C12.29(C2×C6) = C32×M4(2)central extension (φ=1)72C12.29(C2xC6)144,105

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