# Extensions 1→N→G→Q→1 with N=C3×C12 and Q=S3

Direct product G=N×Q with N=C3×C12 and Q=S3
dρLabelID
S3×C3×C1272S3xC3xC12216,136

Semidirect products G=N:Q with N=C3×C12 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C3×C12)⋊1S3 = He34D4φ: S3/C1S3 ⊆ Aut C3×C12366+(C3xC12):1S3216,51
(C3×C12)⋊2S3 = He35D4φ: S3/C1S3 ⊆ Aut C3×C12366(C3xC12):2S3216,68
(C3×C12)⋊3S3 = C4×C32⋊C6φ: S3/C1S3 ⊆ Aut C3×C12366(C3xC12):3S3216,50
(C3×C12)⋊4S3 = C4×He3⋊C2φ: S3/C1S3 ⊆ Aut C3×C12363(C3xC12):4S3216,67
(C3×C12)⋊5S3 = C3312D4φ: S3/C3C2 ⊆ Aut C3×C12108(C3xC12):5S3216,147
(C3×C12)⋊6S3 = C3×C12⋊S3φ: S3/C3C2 ⊆ Aut C3×C1272(C3xC12):6S3216,142
(C3×C12)⋊7S3 = C12×C3⋊S3φ: S3/C3C2 ⊆ Aut C3×C1272(C3xC12):7S3216,141
(C3×C12)⋊8S3 = C4×C33⋊C2φ: S3/C3C2 ⊆ Aut C3×C12108(C3xC12):8S3216,146
(C3×C12)⋊9S3 = C32×D12φ: S3/C3C2 ⊆ Aut C3×C1272(C3xC12):9S3216,137

Non-split extensions G=N.Q with N=C3×C12 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C3×C12).1S3 = He33Q8φ: S3/C1S3 ⊆ Aut C3×C12726-(C3xC12).1S3216,49
(C3×C12).2S3 = C36.C6φ: S3/C1S3 ⊆ Aut C3×C12726-(C3xC12).2S3216,52
(C3×C12).3S3 = D36⋊C3φ: S3/C1S3 ⊆ Aut C3×C12366+(C3xC12).3S3216,54
(C3×C12).4S3 = He34Q8φ: S3/C1S3 ⊆ Aut C3×C12726(C3xC12).4S3216,66
(C3×C12).5S3 = He33C8φ: S3/C1S3 ⊆ Aut C3×C12726(C3xC12).5S3216,14
(C3×C12).6S3 = C9⋊C24φ: S3/C1S3 ⊆ Aut C3×C12726(C3xC12).6S3216,15
(C3×C12).7S3 = He34C8φ: S3/C1S3 ⊆ Aut C3×C12723(C3xC12).7S3216,17
(C3×C12).8S3 = C4×C9⋊C6φ: S3/C1S3 ⊆ Aut C3×C12366(C3xC12).8S3216,53
(C3×C12).9S3 = C12.D9φ: S3/C3C2 ⊆ Aut C3×C12216(C3xC12).9S3216,63
(C3×C12).10S3 = C36⋊S3φ: S3/C3C2 ⊆ Aut C3×C12108(C3xC12).10S3216,65
(C3×C12).11S3 = C338Q8φ: S3/C3C2 ⊆ Aut C3×C12216(C3xC12).11S3216,145
(C3×C12).12S3 = C3×Dic18φ: S3/C3C2 ⊆ Aut C3×C12722(C3xC12).12S3216,43
(C3×C12).13S3 = C3×D36φ: S3/C3C2 ⊆ Aut C3×C12722(C3xC12).13S3216,46
(C3×C12).14S3 = C3×C324Q8φ: S3/C3C2 ⊆ Aut C3×C1272(C3xC12).14S3216,140
(C3×C12).15S3 = C3×C9⋊C8φ: S3/C3C2 ⊆ Aut C3×C12722(C3xC12).15S3216,12
(C3×C12).16S3 = C36.S3φ: S3/C3C2 ⊆ Aut C3×C12216(C3xC12).16S3216,16
(C3×C12).17S3 = C12×D9φ: S3/C3C2 ⊆ Aut C3×C12722(C3xC12).17S3216,45
(C3×C12).18S3 = C4×C9⋊S3φ: S3/C3C2 ⊆ Aut C3×C12108(C3xC12).18S3216,64
(C3×C12).19S3 = C3×C324C8φ: S3/C3C2 ⊆ Aut C3×C1272(C3xC12).19S3216,83
(C3×C12).20S3 = C337C8φ: S3/C3C2 ⊆ Aut C3×C12216(C3xC12).20S3216,84
(C3×C12).21S3 = C32×Dic6φ: S3/C3C2 ⊆ Aut C3×C1272(C3xC12).21S3216,135
(C3×C12).22S3 = C32×C3⋊C8central extension (φ=1)72(C3xC12).22S3216,82

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