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Extensions 1→N→G→Q→1 with N=C3×C4⋊C4 and Q=C6

Direct product G=N×Q with N=C3×C4⋊C4 and Q=C6
dρLabelID
C4⋊C4×C3×C6288C4:C4xC3xC6288,813

Semidirect products G=N:Q with N=C3×C4⋊C4 and Q=C6
extensionφ:Q→Out NdρLabelID
(C3×C4⋊C4)⋊1C6 = C3×C6.D8φ: C6/C3 → C2 ⊆ Out C3×C4⋊C496(C3xC4:C4):1C6288,243
(C3×C4⋊C4)⋊2C6 = C3×S3×C4⋊C4φ: C6/C3 → C2 ⊆ Out C3×C4⋊C496(C3xC4:C4):2C6288,662
(C3×C4⋊C4)⋊3C6 = C3×C4⋊C4⋊7S3φ: C6/C3 → C2 ⊆ Out C3×C4⋊C496(C3xC4:C4):3C6288,663
(C3×C4⋊C4)⋊4C6 = C3×Dic3⋊5D4φ: C6/C3 → C2 ⊆ Out C3×C4⋊C496(C3xC4:C4):4C6288,664
(C3×C4⋊C4)⋊5C6 = C3×D6.D4φ: C6/C3 → C2 ⊆ Out C3×C4⋊C496(C3xC4:C4):5C6288,665
(C3×C4⋊C4)⋊6C6 = C3×C12⋊D4φ: C6/C3 → C2 ⊆ Out C3×C4⋊C496(C3xC4:C4):6C6288,666
(C3×C4⋊C4)⋊7C6 = C3×D6⋊Q8φ: C6/C3 → C2 ⊆ Out C3×C4⋊C496(C3xC4:C4):7C6288,667
(C3×C4⋊C4)⋊8C6 = C3×C4.D12φ: C6/C3 → C2 ⊆ Out C3×C4⋊C496(C3xC4:C4):8C6288,668
(C3×C4⋊C4)⋊9C6 = C3×C4⋊C4⋊S3φ: C6/C3 → C2 ⊆ Out C3×C4⋊C496(C3xC4:C4):9C6288,669
(C3×C4⋊C4)⋊10C6 = C32×D4⋊C4φ: C6/C3 → C2 ⊆ Out C3×C4⋊C4144(C3xC4:C4):10C6288,320
(C3×C4⋊C4)⋊11C6 = C32×C4⋊D4φ: C6/C3 → C2 ⊆ Out C3×C4⋊C4144(C3xC4:C4):11C6288,818
(C3×C4⋊C4)⋊12C6 = C32×C22⋊Q8φ: C6/C3 → C2 ⊆ Out C3×C4⋊C4144(C3xC4:C4):12C6288,819
(C3×C4⋊C4)⋊13C6 = C32×C22.D4φ: C6/C3 → C2 ⊆ Out C3×C4⋊C4144(C3xC4:C4):13C6288,820
(C3×C4⋊C4)⋊14C6 = C32×C42⋊2C2φ: C6/C3 → C2 ⊆ Out C3×C4⋊C4144(C3xC4:C4):14C6288,823
(C3×C4⋊C4)⋊15C6 = C32×C42⋊C2φ: trivial image144(C3xC4:C4):15C6288,814
(C3×C4⋊C4)⋊16C6 = D4×C3×C12φ: trivial image144(C3xC4:C4):16C6288,815

Non-split extensions G=N.Q with N=C3×C4⋊C4 and Q=C6
extensionφ:Q→Out NdρLabelID
(C3×C4⋊C4).1C6 = C3×C6.Q16φ: C6/C3 → C2 ⊆ Out C3×C4⋊C496(C3xC4:C4).1C6288,241
(C3×C4⋊C4).2C6 = C3×C12.Q8φ: C6/C3 → C2 ⊆ Out C3×C4⋊C496(C3xC4:C4).2C6288,242
(C3×C4⋊C4).3C6 = C3×C6.SD16φ: C6/C3 → C2 ⊆ Out C3×C4⋊C496(C3xC4:C4).3C6288,244
(C3×C4⋊C4).4C6 = C3×Dic6⋊C4φ: C6/C3 → C2 ⊆ Out C3×C4⋊C496(C3xC4:C4).4C6288,658
(C3×C4⋊C4).5C6 = C3×C12⋊Q8φ: C6/C3 → C2 ⊆ Out C3×C4⋊C496(C3xC4:C4).5C6288,659
(C3×C4⋊C4).6C6 = C3×Dic3.Q8φ: C6/C3 → C2 ⊆ Out C3×C4⋊C496(C3xC4:C4).6C6288,660
(C3×C4⋊C4).7C6 = C3×C4.Dic6φ: C6/C3 → C2 ⊆ Out C3×C4⋊C496(C3xC4:C4).7C6288,661
(C3×C4⋊C4).8C6 = C9×D4⋊C4φ: C6/C3 → C2 ⊆ Out C3×C4⋊C4144(C3xC4:C4).8C6288,52
(C3×C4⋊C4).9C6 = C9×Q8⋊C4φ: C6/C3 → C2 ⊆ Out C3×C4⋊C4288(C3xC4:C4).9C6288,53
(C3×C4⋊C4).10C6 = C9×C4.Q8φ: C6/C3 → C2 ⊆ Out C3×C4⋊C4288(C3xC4:C4).10C6288,56
(C3×C4⋊C4).11C6 = C9×C2.D8φ: C6/C3 → C2 ⊆ Out C3×C4⋊C4288(C3xC4:C4).11C6288,57
(C3×C4⋊C4).12C6 = C9×C4⋊D4φ: C6/C3 → C2 ⊆ Out C3×C4⋊C4144(C3xC4:C4).12C6288,171
(C3×C4⋊C4).13C6 = C9×C22⋊Q8φ: C6/C3 → C2 ⊆ Out C3×C4⋊C4144(C3xC4:C4).13C6288,172
(C3×C4⋊C4).14C6 = C9×C22.D4φ: C6/C3 → C2 ⊆ Out C3×C4⋊C4144(C3xC4:C4).14C6288,173
(C3×C4⋊C4).15C6 = C9×C42.C2φ: C6/C3 → C2 ⊆ Out C3×C4⋊C4288(C3xC4:C4).15C6288,175
(C3×C4⋊C4).16C6 = C9×C42⋊2C2φ: C6/C3 → C2 ⊆ Out C3×C4⋊C4144(C3xC4:C4).16C6288,176
(C3×C4⋊C4).17C6 = C9×C4⋊Q8φ: C6/C3 → C2 ⊆ Out C3×C4⋊C4288(C3xC4:C4).17C6288,178
(C3×C4⋊C4).18C6 = C32×Q8⋊C4φ: C6/C3 → C2 ⊆ Out C3×C4⋊C4288(C3xC4:C4).18C6288,321
(C3×C4⋊C4).19C6 = C32×C4.Q8φ: C6/C3 → C2 ⊆ Out C3×C4⋊C4288(C3xC4:C4).19C6288,324
(C3×C4⋊C4).20C6 = C32×C2.D8φ: C6/C3 → C2 ⊆ Out C3×C4⋊C4288(C3xC4:C4).20C6288,325
(C3×C4⋊C4).21C6 = C32×C42.C2φ: C6/C3 → C2 ⊆ Out C3×C4⋊C4288(C3xC4:C4).21C6288,822
(C3×C4⋊C4).22C6 = C32×C4⋊Q8φ: C6/C3 → C2 ⊆ Out C3×C4⋊C4288(C3xC4:C4).22C6288,825
(C3×C4⋊C4).23C6 = C4⋊C4×C18φ: trivial image288(C3xC4:C4).23C6288,166
(C3×C4⋊C4).24C6 = C9×C42⋊C2φ: trivial image144(C3xC4:C4).24C6288,167
(C3×C4⋊C4).25C6 = D4×C36φ: trivial image144(C3xC4:C4).25C6288,168
(C3×C4⋊C4).26C6 = Q8×C36φ: trivial image288(C3xC4:C4).26C6288,169
(C3×C4⋊C4).27C6 = Q8×C3×C12φ: trivial image288(C3xC4:C4).27C6288,816

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