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Extensions 1→N→G→Q→1 with N=C4 and Q=C6×C12

Direct product G=N×Q with N=C4 and Q=C6×C12
dρLabelID
C2×C122288C2xC12^2288,811

Semidirect products G=N:Q with N=C4 and Q=C6×C12
extensionφ:Q→Aut NdρLabelID
C4⋊1(C6×C12) = D4×C3×C12φ: C6×C12/C3×C12 → C2 ⊆ Aut C4144C4:1(C6xC12)288,815
C4⋊2(C6×C12) = C4⋊C4×C3×C6φ: C6×C12/C62 → C2 ⊆ Aut C4288C4:2(C6xC12)288,813

Non-split extensions G=N.Q with N=C4 and Q=C6×C12
extensionφ:Q→Aut NdρLabelID
C4.1(C6×C12) = C32×D4⋊C4φ: C6×C12/C3×C12 → C2 ⊆ Aut C4144C4.1(C6xC12)288,320
C4.2(C6×C12) = C32×Q8⋊C4φ: C6×C12/C3×C12 → C2 ⊆ Aut C4288C4.2(C6xC12)288,321
C4.3(C6×C12) = C32×C4≀C2φ: C6×C12/C3×C12 → C2 ⊆ Aut C472C4.3(C6xC12)288,322
C4.4(C6×C12) = Q8×C3×C12φ: C6×C12/C3×C12 → C2 ⊆ Aut C4288C4.4(C6xC12)288,816
C4.5(C6×C12) = C32×C8○D4φ: C6×C12/C3×C12 → C2 ⊆ Aut C4144C4.5(C6xC12)288,828
C4.6(C6×C12) = C32×C4.Q8φ: C6×C12/C62 → C2 ⊆ Aut C4288C4.6(C6xC12)288,324
C4.7(C6×C12) = C32×C2.D8φ: C6×C12/C62 → C2 ⊆ Aut C4288C4.7(C6xC12)288,325
C4.8(C6×C12) = C32×C8.C4φ: C6×C12/C62 → C2 ⊆ Aut C4144C4.8(C6xC12)288,326
C4.9(C6×C12) = C32×C8⋊C4central extension (φ=1)288C4.9(C6xC12)288,315
C4.10(C6×C12) = C32×M5(2)central extension (φ=1)144C4.10(C6xC12)288,328
C4.11(C6×C12) = C32×C42⋊C2central extension (φ=1)144C4.11(C6xC12)288,814
C4.12(C6×C12) = M4(2)×C3×C6central extension (φ=1)144C4.12(C6xC12)288,827

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