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Extensions 1→N→G→Q→1 with N=C3×C6 and Q=M4(2)

Direct product G=N×Q with N=C3×C6 and Q=M4(2)
dρLabelID
M4(2)×C3×C6144M4(2)xC3xC6288,827

Semidirect products G=N:Q with N=C3×C6 and Q=M4(2)
extensionφ:Q→Aut NdρLabelID
(C3×C6)⋊1M4(2) = C2×C32⋊M4(2)φ: M4(2)/C4 → C4 ⊆ Aut C3×C648(C3xC6):1M4(2)288,930
(C3×C6)⋊2M4(2) = C2×D6.Dic3φ: M4(2)/C4 → C22 ⊆ Aut C3×C696(C3xC6):2M4(2)288,467
(C3×C6)⋊3M4(2) = C2×C12.31D6φ: M4(2)/C4 → C22 ⊆ Aut C3×C648(C3xC6):3M4(2)288,468
(C3×C6)⋊4M4(2) = C2×C62.C4φ: M4(2)/C22 → C4 ⊆ Aut C3×C648(C3xC6):4M4(2)288,940
(C3×C6)⋊5M4(2) = C6×C8⋊S3φ: M4(2)/C8 → C2 ⊆ Aut C3×C696(C3xC6):5M4(2)288,671
(C3×C6)⋊6M4(2) = C2×C24⋊S3φ: M4(2)/C8 → C2 ⊆ Aut C3×C6144(C3xC6):6M4(2)288,757
(C3×C6)⋊7M4(2) = C6×C4.Dic3φ: M4(2)/C2×C4 → C2 ⊆ Aut C3×C648(C3xC6):7M4(2)288,692
(C3×C6)⋊8M4(2) = C2×C12.58D6φ: M4(2)/C2×C4 → C2 ⊆ Aut C3×C6144(C3xC6):8M4(2)288,778

Non-split extensions G=N.Q with N=C3×C6 and Q=M4(2)
extensionφ:Q→Aut NdρLabelID
(C3×C6).1M4(2) = (C3×C12)⋊4C8φ: M4(2)/C4 → C4 ⊆ Aut C3×C696(C3xC6).1M4(2)288,424
(C3×C6).2M4(2) = C62.6(C2×C4)φ: M4(2)/C4 → C4 ⊆ Aut C3×C648(C3xC6).2M4(2)288,426
(C3×C6).3M4(2) = C3⋊C8⋊Dic3φ: M4(2)/C4 → C22 ⊆ Aut C3×C696(C3xC6).3M4(2)288,202
(C3×C6).4M4(2) = C2.Dic32φ: M4(2)/C4 → C22 ⊆ Aut C3×C696(C3xC6).4M4(2)288,203
(C3×C6).5M4(2) = C12.77D12φ: M4(2)/C4 → C22 ⊆ Aut C3×C696(C3xC6).5M4(2)288,204
(C3×C6).6M4(2) = C12.78D12φ: M4(2)/C4 → C22 ⊆ Aut C3×C648(C3xC6).6M4(2)288,205
(C3×C6).7M4(2) = C12.81D12φ: M4(2)/C4 → C22 ⊆ Aut C3×C696(C3xC6).7M4(2)288,219
(C3×C6).8M4(2) = C12.15Dic6φ: M4(2)/C4 → C22 ⊆ Aut C3×C696(C3xC6).8M4(2)288,220
(C3×C6).9M4(2) = C32⋊2C8⋊C4φ: M4(2)/C22 → C4 ⊆ Aut C3×C696(C3xC6).9M4(2)288,425
(C3×C6).10M4(2) = C32⋊5(C4⋊C8)φ: M4(2)/C22 → C4 ⊆ Aut C3×C696(C3xC6).10M4(2)288,427
(C3×C6).11M4(2) = C62⋊3C8φ: M4(2)/C22 → C4 ⊆ Aut C3×C648(C3xC6).11M4(2)288,435
(C3×C6).12M4(2) = C3×Dic3⋊C8φ: M4(2)/C8 → C2 ⊆ Aut C3×C696(C3xC6).12M4(2)288,248
(C3×C6).13M4(2) = C3×C24⋊C4φ: M4(2)/C8 → C2 ⊆ Aut C3×C696(C3xC6).13M4(2)288,249
(C3×C6).14M4(2) = C3×D6⋊C8φ: M4(2)/C8 → C2 ⊆ Aut C3×C696(C3xC6).14M4(2)288,254
(C3×C6).15M4(2) = C12.30Dic6φ: M4(2)/C8 → C2 ⊆ Aut C3×C6288(C3xC6).15M4(2)288,289
(C3×C6).16M4(2) = C24⋊Dic3φ: M4(2)/C8 → C2 ⊆ Aut C3×C6288(C3xC6).16M4(2)288,290
(C3×C6).17M4(2) = C12.60D12φ: M4(2)/C8 → C2 ⊆ Aut C3×C6144(C3xC6).17M4(2)288,295
(C3×C6).18M4(2) = C3×C42.S3φ: M4(2)/C2×C4 → C2 ⊆ Aut C3×C696(C3xC6).18M4(2)288,237
(C3×C6).19M4(2) = C3×C12⋊C8φ: M4(2)/C2×C4 → C2 ⊆ Aut C3×C696(C3xC6).19M4(2)288,238
(C3×C6).20M4(2) = C3×C12.55D4φ: M4(2)/C2×C4 → C2 ⊆ Aut C3×C648(C3xC6).20M4(2)288,264
(C3×C6).21M4(2) = C122.C2φ: M4(2)/C2×C4 → C2 ⊆ Aut C3×C6288(C3xC6).21M4(2)288,278
(C3×C6).22M4(2) = C12.57D12φ: M4(2)/C2×C4 → C2 ⊆ Aut C3×C6288(C3xC6).22M4(2)288,279
(C3×C6).23M4(2) = C62⋊7C8φ: M4(2)/C2×C4 → C2 ⊆ Aut C3×C6144(C3xC6).23M4(2)288,305
(C3×C6).24M4(2) = C32×C8⋊C4central extension (φ=1)288(C3xC6).24M4(2)288,315
(C3×C6).25M4(2) = C32×C22⋊C8central extension (φ=1)144(C3xC6).25M4(2)288,316
(C3×C6).26M4(2) = C32×C4⋊C8central extension (φ=1)288(C3xC6).26M4(2)288,323

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