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Extensions 1→N→G→Q→1 with N=C3×C4⋊C4 and Q=S3

Direct product G=N×Q with N=C3×C4⋊C4 and Q=S3
dρLabelID
C3×S3×C4⋊C496C3xS3xC4:C4288,662

Semidirect products G=N:Q with N=C3×C4⋊C4 and Q=S3
extensionφ:Q→Out NdρLabelID
(C3×C4⋊C4)⋊1S3 = C62.113D4φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4144(C3xC4:C4):1S3288,284
(C3×C4⋊C4)⋊2S3 = C4⋊C4×C3⋊S3φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4144(C3xC4:C4):2S3288,748
(C3×C4⋊C4)⋊3S3 = C62.236C23φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4144(C3xC4:C4):3S3288,749
(C3×C4⋊C4)⋊4S3 = C62.237C23φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4144(C3xC4:C4):4S3288,750
(C3×C4⋊C4)⋊5S3 = C62.238C23φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4144(C3xC4:C4):5S3288,751
(C3×C4⋊C4)⋊6S3 = C12⋊3D12φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4144(C3xC4:C4):6S3288,752
(C3×C4⋊C4)⋊7S3 = C62.240C23φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4144(C3xC4:C4):7S3288,753
(C3×C4⋊C4)⋊8S3 = C12.31D12φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4144(C3xC4:C4):8S3288,754
(C3×C4⋊C4)⋊9S3 = C62.242C23φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4144(C3xC4:C4):9S3288,755
(C3×C4⋊C4)⋊10S3 = C3×C6.D8φ: S3/C3 → C2 ⊆ Out C3×C4⋊C496(C3xC4:C4):10S3288,243
(C3×C4⋊C4)⋊11S3 = C3×D6.D4φ: S3/C3 → C2 ⊆ Out C3×C4⋊C496(C3xC4:C4):11S3288,665
(C3×C4⋊C4)⋊12S3 = C3×C12⋊D4φ: S3/C3 → C2 ⊆ Out C3×C4⋊C496(C3xC4:C4):12S3288,666
(C3×C4⋊C4)⋊13S3 = C3×D6⋊Q8φ: S3/C3 → C2 ⊆ Out C3×C4⋊C496(C3xC4:C4):13S3288,667
(C3×C4⋊C4)⋊14S3 = C3×C4.D12φ: S3/C3 → C2 ⊆ Out C3×C4⋊C496(C3xC4:C4):14S3288,668
(C3×C4⋊C4)⋊15S3 = C3×C4⋊C4⋊S3φ: S3/C3 → C2 ⊆ Out C3×C4⋊C496(C3xC4:C4):15S3288,669
(C3×C4⋊C4)⋊16S3 = C3×C4⋊C4⋊7S3φ: trivial image96(C3xC4:C4):16S3288,663
(C3×C4⋊C4)⋊17S3 = C3×Dic3⋊5D4φ: trivial image96(C3xC4:C4):17S3288,664

Non-split extensions G=N.Q with N=C3×C4⋊C4 and Q=S3
extensionφ:Q→Out NdρLabelID
(C3×C4⋊C4).1S3 = C36.Q8φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4288(C3xC4:C4).1S3288,14
(C3×C4⋊C4).2S3 = C4.Dic18φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4288(C3xC4:C4).2S3288,15
(C3×C4⋊C4).3S3 = C18.Q16φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4288(C3xC4:C4).3S3288,16
(C3×C4⋊C4).4S3 = C18.D8φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4144(C3xC4:C4).4S3288,17
(C3×C4⋊C4).5S3 = Dic9⋊3Q8φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4288(C3xC4:C4).5S3288,97
(C3×C4⋊C4).6S3 = C36⋊Q8φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4288(C3xC4:C4).6S3288,98
(C3×C4⋊C4).7S3 = Dic9.Q8φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4288(C3xC4:C4).7S3288,99
(C3×C4⋊C4).8S3 = C36.3Q8φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4288(C3xC4:C4).8S3288,100
(C3×C4⋊C4).9S3 = C4⋊C4×D9φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4144(C3xC4:C4).9S3288,101
(C3×C4⋊C4).10S3 = C4⋊C4⋊7D9φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4144(C3xC4:C4).10S3288,102
(C3×C4⋊C4).11S3 = D36⋊C4φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4144(C3xC4:C4).11S3288,103
(C3×C4⋊C4).12S3 = D18.D4φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4144(C3xC4:C4).12S3288,104
(C3×C4⋊C4).13S3 = C4⋊D36φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4144(C3xC4:C4).13S3288,105
(C3×C4⋊C4).14S3 = D18⋊Q8φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4144(C3xC4:C4).14S3288,106
(C3×C4⋊C4).15S3 = D18⋊2Q8φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4144(C3xC4:C4).15S3288,107
(C3×C4⋊C4).16S3 = C4⋊C4⋊D9φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4144(C3xC4:C4).16S3288,108
(C3×C4⋊C4).17S3 = C12.9Dic6φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4288(C3xC4:C4).17S3288,282
(C3×C4⋊C4).18S3 = C12.10Dic6φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4288(C3xC4:C4).18S3288,283
(C3×C4⋊C4).19S3 = C62.114D4φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4288(C3xC4:C4).19S3288,285
(C3×C4⋊C4).20S3 = C62.231C23φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4288(C3xC4:C4).20S3288,744
(C3×C4⋊C4).21S3 = C12⋊2Dic6φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4288(C3xC4:C4).21S3288,745
(C3×C4⋊C4).22S3 = C62.233C23φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4288(C3xC4:C4).22S3288,746
(C3×C4⋊C4).23S3 = C62.234C23φ: S3/C3 → C2 ⊆ Out C3×C4⋊C4288(C3xC4:C4).23S3288,747
(C3×C4⋊C4).24S3 = C3×C6.Q16φ: S3/C3 → C2 ⊆ Out C3×C4⋊C496(C3xC4:C4).24S3288,241
(C3×C4⋊C4).25S3 = C3×C12.Q8φ: S3/C3 → C2 ⊆ Out C3×C4⋊C496(C3xC4:C4).25S3288,242
(C3×C4⋊C4).26S3 = C3×C6.SD16φ: S3/C3 → C2 ⊆ Out C3×C4⋊C496(C3xC4:C4).26S3288,244
(C3×C4⋊C4).27S3 = C3×C12⋊Q8φ: S3/C3 → C2 ⊆ Out C3×C4⋊C496(C3xC4:C4).27S3288,659
(C3×C4⋊C4).28S3 = C3×Dic3.Q8φ: S3/C3 → C2 ⊆ Out C3×C4⋊C496(C3xC4:C4).28S3288,660
(C3×C4⋊C4).29S3 = C3×C4.Dic6φ: S3/C3 → C2 ⊆ Out C3×C4⋊C496(C3xC4:C4).29S3288,661
(C3×C4⋊C4).30S3 = C3×Dic6⋊C4φ: trivial image96(C3xC4:C4).30S3288,658

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