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

Direct product G=N×Q with N=C6 and Q=C2×C6

Semidirect products G=N:Q with N=C6 and Q=C2×C6
extensionφ:Q→Aut NdρLabelID
C6⋊(C2×C6) = S3×C2×C6φ: C2×C6/C6C2 ⊆ Aut C624C6:(C2xC6)72,48

Non-split extensions G=N.Q with N=C6 and Q=C2×C6
extensionφ:Q→Aut NdρLabelID
C6.1(C2×C6) = C3×Dic6φ: C2×C6/C6C2 ⊆ Aut C6242C6.1(C2xC6)72,26
C6.2(C2×C6) = S3×C12φ: C2×C6/C6C2 ⊆ Aut C6242C6.2(C2xC6)72,27
C6.3(C2×C6) = C3×D12φ: C2×C6/C6C2 ⊆ Aut C6242C6.3(C2xC6)72,28
C6.4(C2×C6) = C6×Dic3φ: C2×C6/C6C2 ⊆ Aut C624C6.4(C2xC6)72,29
C6.5(C2×C6) = C3×C3⋊D4φ: C2×C6/C6C2 ⊆ Aut C6122C6.5(C2xC6)72,30
C6.6(C2×C6) = D4×C9central extension (φ=1)362C6.6(C2xC6)72,10
C6.7(C2×C6) = Q8×C9central extension (φ=1)722C6.7(C2xC6)72,11
C6.8(C2×C6) = D4×C32central extension (φ=1)36C6.8(C2xC6)72,37
C6.9(C2×C6) = Q8×C32central extension (φ=1)72C6.9(C2xC6)72,38