# Extensions 1→N→G→Q→1 with N=C3×C6 and Q=D6

Direct product G=N×Q with N=C3×C6 and Q=D6
dρLabelID
S3×C6272S3xC6^2216,174

Semidirect products G=N:Q with N=C3×C6 and Q=D6
extensionφ:Q→Aut NdρLabelID
(C3×C6)⋊D6 = C2×C32⋊D6φ: D6/C1D6 ⊆ Aut C3×C6186+(C3xC6):D6216,102
(C3×C6)⋊2D6 = C22×C32⋊C6φ: D6/C2S3 ⊆ Aut C3×C636(C3xC6):2D6216,110
(C3×C6)⋊3D6 = C22×He3⋊C2φ: D6/C2S3 ⊆ Aut C3×C636(C3xC6):3D6216,113
(C3×C6)⋊4D6 = C2×S3×C3⋊S3φ: D6/C3C22 ⊆ Aut C3×C636(C3xC6):4D6216,171
(C3×C6)⋊5D6 = C2×C324D6φ: D6/C3C22 ⊆ Aut C3×C6244(C3xC6):5D6216,172
(C3×C6)⋊6D6 = S32×C6φ: D6/S3C2 ⊆ Aut C3×C6244(C3xC6):6D6216,170
(C3×C6)⋊7D6 = C2×C6×C3⋊S3φ: D6/C6C2 ⊆ Aut C3×C672(C3xC6):7D6216,175
(C3×C6)⋊8D6 = C22×C33⋊C2φ: D6/C6C2 ⊆ Aut C3×C6108(C3xC6):8D6216,176

Non-split extensions G=N.Q with N=C3×C6 and Q=D6
extensionφ:Q→Aut NdρLabelID
(C3×C6).1D6 = He32Q8φ: D6/C1D6 ⊆ Aut C3×C6726-(C3xC6).1D6216,33
(C3×C6).2D6 = C6.S32φ: D6/C1D6 ⊆ Aut C3×C6366(C3xC6).2D6216,34
(C3×C6).3D6 = He32D4φ: D6/C1D6 ⊆ Aut C3×C6366+(C3xC6).3D6216,35
(C3×C6).4D6 = He3⋊(C2×C4)φ: D6/C1D6 ⊆ Aut C3×C6366-(C3xC6).4D6216,36
(C3×C6).5D6 = He33D4φ: D6/C1D6 ⊆ Aut C3×C6366(C3xC6).5D6216,37
(C3×C6).6D6 = He33Q8φ: D6/C2S3 ⊆ Aut C3×C6726-(C3xC6).6D6216,49
(C3×C6).7D6 = C4×C32⋊C6φ: D6/C2S3 ⊆ Aut C3×C6366(C3xC6).7D6216,50
(C3×C6).8D6 = He34D4φ: D6/C2S3 ⊆ Aut C3×C6366+(C3xC6).8D6216,51
(C3×C6).9D6 = C36.C6φ: D6/C2S3 ⊆ Aut C3×C6726-(C3xC6).9D6216,52
(C3×C6).10D6 = C4×C9⋊C6φ: D6/C2S3 ⊆ Aut C3×C6366(C3xC6).10D6216,53
(C3×C6).11D6 = D36⋊C3φ: D6/C2S3 ⊆ Aut C3×C6366+(C3xC6).11D6216,54
(C3×C6).12D6 = C2×C32⋊C12φ: D6/C2S3 ⊆ Aut C3×C672(C3xC6).12D6216,59
(C3×C6).13D6 = He36D4φ: D6/C2S3 ⊆ Aut C3×C6366(C3xC6).13D6216,60
(C3×C6).14D6 = C2×C9⋊C12φ: D6/C2S3 ⊆ Aut C3×C672(C3xC6).14D6216,61
(C3×C6).15D6 = Dic9⋊C6φ: D6/C2S3 ⊆ Aut C3×C6366(C3xC6).15D6216,62
(C3×C6).16D6 = He34Q8φ: D6/C2S3 ⊆ Aut C3×C6726(C3xC6).16D6216,66
(C3×C6).17D6 = C4×He3⋊C2φ: D6/C2S3 ⊆ Aut C3×C6363(C3xC6).17D6216,67
(C3×C6).18D6 = He35D4φ: D6/C2S3 ⊆ Aut C3×C6366(C3xC6).18D6216,68
(C3×C6).19D6 = C2×He33C4φ: D6/C2S3 ⊆ Aut C3×C672(C3xC6).19D6216,71
(C3×C6).20D6 = He37D4φ: D6/C2S3 ⊆ Aut C3×C6366(C3xC6).20D6216,72
(C3×C6).21D6 = C22×C9⋊C6φ: D6/C2S3 ⊆ Aut C3×C636(C3xC6).21D6216,111
(C3×C6).22D6 = C9⋊Dic6φ: D6/C3C22 ⊆ Aut C3×C6724-(C3xC6).22D6216,26
(C3×C6).23D6 = Dic3×D9φ: D6/C3C22 ⊆ Aut C3×C6724-(C3xC6).23D6216,27
(C3×C6).24D6 = C18.D6φ: D6/C3C22 ⊆ Aut C3×C6364+(C3xC6).24D6216,28
(C3×C6).25D6 = C3⋊D36φ: D6/C3C22 ⊆ Aut C3×C6364+(C3xC6).25D6216,29
(C3×C6).26D6 = S3×Dic9φ: D6/C3C22 ⊆ Aut C3×C6724-(C3xC6).26D6216,30
(C3×C6).27D6 = D6⋊D9φ: D6/C3C22 ⊆ Aut C3×C6724-(C3xC6).27D6216,31
(C3×C6).28D6 = C9⋊D12φ: D6/C3C22 ⊆ Aut C3×C6364+(C3xC6).28D6216,32
(C3×C6).29D6 = C2×S3×D9φ: D6/C3C22 ⊆ Aut C3×C6364+(C3xC6).29D6216,101
(C3×C6).30D6 = C338(C2×C4)φ: D6/C3C22 ⊆ Aut C3×C636(C3xC6).30D6216,126
(C3×C6).31D6 = C336D4φ: D6/C3C22 ⊆ Aut C3×C672(C3xC6).31D6216,127
(C3×C6).32D6 = C337D4φ: D6/C3C22 ⊆ Aut C3×C636(C3xC6).32D6216,128
(C3×C6).33D6 = C338D4φ: D6/C3C22 ⊆ Aut C3×C636(C3xC6).33D6216,129
(C3×C6).34D6 = C334Q8φ: D6/C3C22 ⊆ Aut C3×C672(C3xC6).34D6216,130
(C3×C6).35D6 = C339(C2×C4)φ: D6/C3C22 ⊆ Aut C3×C6244(C3xC6).35D6216,131
(C3×C6).36D6 = C339D4φ: D6/C3C22 ⊆ Aut C3×C6244(C3xC6).36D6216,132
(C3×C6).37D6 = C335Q8φ: D6/C3C22 ⊆ Aut C3×C6244(C3xC6).37D6216,133
(C3×C6).38D6 = C3×S3×Dic3φ: D6/S3C2 ⊆ Aut C3×C6244(C3xC6).38D6216,119
(C3×C6).39D6 = C3×C6.D6φ: D6/S3C2 ⊆ Aut C3×C6244(C3xC6).39D6216,120
(C3×C6).40D6 = C3×D6⋊S3φ: D6/S3C2 ⊆ Aut C3×C6244(C3xC6).40D6216,121
(C3×C6).41D6 = C3×C3⋊D12φ: D6/S3C2 ⊆ Aut C3×C6244(C3xC6).41D6216,122
(C3×C6).42D6 = C3×C322Q8φ: D6/S3C2 ⊆ Aut C3×C6244(C3xC6).42D6216,123
(C3×C6).43D6 = S3×C3⋊Dic3φ: D6/S3C2 ⊆ Aut C3×C672(C3xC6).43D6216,124
(C3×C6).44D6 = Dic3×C3⋊S3φ: D6/S3C2 ⊆ Aut C3×C672(C3xC6).44D6216,125
(C3×C6).45D6 = C3×Dic18φ: D6/C6C2 ⊆ Aut C3×C6722(C3xC6).45D6216,43
(C3×C6).46D6 = C12×D9φ: D6/C6C2 ⊆ Aut C3×C6722(C3xC6).46D6216,45
(C3×C6).47D6 = C3×D36φ: D6/C6C2 ⊆ Aut C3×C6722(C3xC6).47D6216,46
(C3×C6).48D6 = C6×Dic9φ: D6/C6C2 ⊆ Aut C3×C672(C3xC6).48D6216,55
(C3×C6).49D6 = C3×C9⋊D4φ: D6/C6C2 ⊆ Aut C3×C6362(C3xC6).49D6216,57
(C3×C6).50D6 = C12.D9φ: D6/C6C2 ⊆ Aut C3×C6216(C3xC6).50D6216,63
(C3×C6).51D6 = C4×C9⋊S3φ: D6/C6C2 ⊆ Aut C3×C6108(C3xC6).51D6216,64
(C3×C6).52D6 = C36⋊S3φ: D6/C6C2 ⊆ Aut C3×C6108(C3xC6).52D6216,65
(C3×C6).53D6 = C2×C9⋊Dic3φ: D6/C6C2 ⊆ Aut C3×C6216(C3xC6).53D6216,69
(C3×C6).54D6 = C6.D18φ: D6/C6C2 ⊆ Aut C3×C6108(C3xC6).54D6216,70
(C3×C6).55D6 = C2×C6×D9φ: D6/C6C2 ⊆ Aut C3×C672(C3xC6).55D6216,108
(C3×C6).56D6 = C22×C9⋊S3φ: D6/C6C2 ⊆ Aut C3×C6108(C3xC6).56D6216,112
(C3×C6).57D6 = C3×C324Q8φ: D6/C6C2 ⊆ Aut C3×C672(C3xC6).57D6216,140
(C3×C6).58D6 = C12×C3⋊S3φ: D6/C6C2 ⊆ Aut C3×C672(C3xC6).58D6216,141
(C3×C6).59D6 = C3×C12⋊S3φ: D6/C6C2 ⊆ Aut C3×C672(C3xC6).59D6216,142
(C3×C6).60D6 = C6×C3⋊Dic3φ: D6/C6C2 ⊆ Aut C3×C672(C3xC6).60D6216,143
(C3×C6).61D6 = C3×C327D4φ: D6/C6C2 ⊆ Aut C3×C636(C3xC6).61D6216,144
(C3×C6).62D6 = C338Q8φ: D6/C6C2 ⊆ Aut C3×C6216(C3xC6).62D6216,145
(C3×C6).63D6 = C4×C33⋊C2φ: D6/C6C2 ⊆ Aut C3×C6108(C3xC6).63D6216,146
(C3×C6).64D6 = C3312D4φ: D6/C6C2 ⊆ Aut C3×C6108(C3xC6).64D6216,147
(C3×C6).65D6 = C2×C335C4φ: D6/C6C2 ⊆ Aut C3×C6216(C3xC6).65D6216,148
(C3×C6).66D6 = C3315D4φ: D6/C6C2 ⊆ Aut C3×C6108(C3xC6).66D6216,149
(C3×C6).67D6 = C32×Dic6central extension (φ=1)72(C3xC6).67D6216,135
(C3×C6).68D6 = S3×C3×C12central extension (φ=1)72(C3xC6).68D6216,136
(C3×C6).69D6 = C32×D12central extension (φ=1)72(C3xC6).69D6216,137
(C3×C6).70D6 = Dic3×C3×C6central extension (φ=1)72(C3xC6).70D6216,138
(C3×C6).71D6 = C32×C3⋊D4central extension (φ=1)36(C3xC6).71D6216,139

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