Extensions 1→N→G→Q→1 with N=C3×C6 and Q=D4

Direct product G=N×Q with N=C3×C6 and Q=D4
dρLabelID
D4×C3×C672D4xC3xC6144,179

Semidirect products G=N:Q with N=C3×C6 and Q=D4
extensionφ:Q→Aut NdρLabelID
(C3×C6)⋊D4 = C2×S3≀C2φ: D4/C1D4 ⊆ Aut C3×C6124+(C3xC6):D4144,186
(C3×C6)⋊2D4 = C2×D6⋊S3φ: D4/C2C22 ⊆ Aut C3×C648(C3xC6):2D4144,150
(C3×C6)⋊3D4 = C2×C3⋊D12φ: D4/C2C22 ⊆ Aut C3×C624(C3xC6):3D4144,151
(C3×C6)⋊4D4 = C6×D12φ: D4/C4C2 ⊆ Aut C3×C648(C3xC6):4D4144,160
(C3×C6)⋊5D4 = C2×C12⋊S3φ: D4/C4C2 ⊆ Aut C3×C672(C3xC6):5D4144,170
(C3×C6)⋊6D4 = C6×C3⋊D4φ: D4/C22C2 ⊆ Aut C3×C624(C3xC6):6D4144,167
(C3×C6)⋊7D4 = C2×C327D4φ: D4/C22C2 ⊆ Aut C3×C672(C3xC6):7D4144,177

Non-split extensions G=N.Q with N=C3×C6 and Q=D4
extensionφ:Q→Aut NdρLabelID
(C3×C6).1D4 = S32⋊C4φ: D4/C1D4 ⊆ Aut C3×C6124+(C3xC6).1D4144,115
(C3×C6).2D4 = C3⋊S3.Q8φ: D4/C1D4 ⊆ Aut C3×C6244(C3xC6).2D4144,116
(C3×C6).3D4 = C32⋊D8φ: D4/C1D4 ⊆ Aut C3×C6244(C3xC6).3D4144,117
(C3×C6).4D4 = C322SD16φ: D4/C1D4 ⊆ Aut C3×C6244-(C3xC6).4D4144,118
(C3×C6).5D4 = C32⋊Q16φ: D4/C1D4 ⊆ Aut C3×C6484-(C3xC6).5D4144,119
(C3×C6).6D4 = C322D8φ: D4/C2C22 ⊆ Aut C3×C6484(C3xC6).6D4144,56
(C3×C6).7D4 = C3⋊D24φ: D4/C2C22 ⊆ Aut C3×C6244+(C3xC6).7D4144,57
(C3×C6).8D4 = Dic6⋊S3φ: D4/C2C22 ⊆ Aut C3×C6484(C3xC6).8D4144,58
(C3×C6).9D4 = D12.S3φ: D4/C2C22 ⊆ Aut C3×C6484-(C3xC6).9D4144,59
(C3×C6).10D4 = C325SD16φ: D4/C2C22 ⊆ Aut C3×C6244+(C3xC6).10D4144,60
(C3×C6).11D4 = C322Q16φ: D4/C2C22 ⊆ Aut C3×C6484(C3xC6).11D4144,61
(C3×C6).12D4 = C323Q16φ: D4/C2C22 ⊆ Aut C3×C6484-(C3xC6).12D4144,62
(C3×C6).13D4 = D6⋊Dic3φ: D4/C2C22 ⊆ Aut C3×C648(C3xC6).13D4144,64
(C3×C6).14D4 = C6.D12φ: D4/C2C22 ⊆ Aut C3×C624(C3xC6).14D4144,65
(C3×C6).15D4 = Dic3⋊Dic3φ: D4/C2C22 ⊆ Aut C3×C648(C3xC6).15D4144,66
(C3×C6).16D4 = C62.C22φ: D4/C2C22 ⊆ Aut C3×C648(C3xC6).16D4144,67
(C3×C6).17D4 = C3×C24⋊C2φ: D4/C4C2 ⊆ Aut C3×C6482(C3xC6).17D4144,71
(C3×C6).18D4 = C3×D24φ: D4/C4C2 ⊆ Aut C3×C6482(C3xC6).18D4144,72
(C3×C6).19D4 = C3×Dic12φ: D4/C4C2 ⊆ Aut C3×C6482(C3xC6).19D4144,73
(C3×C6).20D4 = C3×C4⋊Dic3φ: D4/C4C2 ⊆ Aut C3×C648(C3xC6).20D4144,78
(C3×C6).21D4 = C3×D6⋊C4φ: D4/C4C2 ⊆ Aut C3×C648(C3xC6).21D4144,79
(C3×C6).22D4 = C242S3φ: D4/C4C2 ⊆ Aut C3×C672(C3xC6).22D4144,87
(C3×C6).23D4 = C325D8φ: D4/C4C2 ⊆ Aut C3×C672(C3xC6).23D4144,88
(C3×C6).24D4 = C325Q16φ: D4/C4C2 ⊆ Aut C3×C6144(C3xC6).24D4144,89
(C3×C6).25D4 = C12⋊Dic3φ: D4/C4C2 ⊆ Aut C3×C6144(C3xC6).25D4144,94
(C3×C6).26D4 = C6.11D12φ: D4/C4C2 ⊆ Aut C3×C672(C3xC6).26D4144,95
(C3×C6).27D4 = C3×Dic3⋊C4φ: D4/C22C2 ⊆ Aut C3×C648(C3xC6).27D4144,77
(C3×C6).28D4 = C3×D4⋊S3φ: D4/C22C2 ⊆ Aut C3×C6244(C3xC6).28D4144,80
(C3×C6).29D4 = C3×D4.S3φ: D4/C22C2 ⊆ Aut C3×C6244(C3xC6).29D4144,81
(C3×C6).30D4 = C3×Q82S3φ: D4/C22C2 ⊆ Aut C3×C6484(C3xC6).30D4144,82
(C3×C6).31D4 = C3×C3⋊Q16φ: D4/C22C2 ⊆ Aut C3×C6484(C3xC6).31D4144,83
(C3×C6).32D4 = C3×C6.D4φ: D4/C22C2 ⊆ Aut C3×C624(C3xC6).32D4144,84
(C3×C6).33D4 = C6.Dic6φ: D4/C22C2 ⊆ Aut C3×C6144(C3xC6).33D4144,93
(C3×C6).34D4 = C327D8φ: D4/C22C2 ⊆ Aut C3×C672(C3xC6).34D4144,96
(C3×C6).35D4 = C329SD16φ: D4/C22C2 ⊆ Aut C3×C672(C3xC6).35D4144,97
(C3×C6).36D4 = C3211SD16φ: D4/C22C2 ⊆ Aut C3×C672(C3xC6).36D4144,98
(C3×C6).37D4 = C327Q16φ: D4/C22C2 ⊆ Aut C3×C6144(C3xC6).37D4144,99
(C3×C6).38D4 = C625C4φ: D4/C22C2 ⊆ Aut C3×C672(C3xC6).38D4144,100
(C3×C6).39D4 = C32×C22⋊C4central extension (φ=1)72(C3xC6).39D4144,102
(C3×C6).40D4 = C32×C4⋊C4central extension (φ=1)144(C3xC6).40D4144,103
(C3×C6).41D4 = C32×D8central extension (φ=1)72(C3xC6).41D4144,106
(C3×C6).42D4 = C32×SD16central extension (φ=1)72(C3xC6).42D4144,107
(C3×C6).43D4 = C32×Q16central extension (φ=1)144(C3xC6).43D4144,108

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