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Extensions 1→N→G→Q→1 with N=C32×C6 and Q=S3

Direct product G=N×Q with N=C32×C6 and Q=S3
dρLabelID
S3×C32×C6108S3xC3^2xC6324,172

Semidirect products G=N:Q with N=C32×C6 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C32×C6)⋊1S3 = C2×C3≀S3φ: S3/C1 → S3 ⊆ Aut C32×C6183(C3^2xC6):1S3324,68
(C32×C6)⋊2S3 = C2×C33⋊S3φ: S3/C1 → S3 ⊆ Aut C32×C6186+(C3^2xC6):2S3324,77
(C32×C6)⋊3S3 = C6×C32⋊C6φ: S3/C1 → S3 ⊆ Aut C32×C6366(C3^2xC6):3S3324,138
(C32×C6)⋊4S3 = C2×He3⋊4S3φ: S3/C1 → S3 ⊆ Aut C32×C654(C3^2xC6):4S3324,144
(C32×C6)⋊5S3 = C6×He3⋊C2φ: S3/C1 → S3 ⊆ Aut C32×C654(C3^2xC6):5S3324,145
(C32×C6)⋊6S3 = C2×He3⋊5S3φ: S3/C1 → S3 ⊆ Aut C32×C6366(C3^2xC6):6S3324,150
(C32×C6)⋊7S3 = C3⋊S3×C3×C6φ: S3/C3 → C2 ⊆ Aut C32×C636(C3^2xC6):7S3324,173
(C32×C6)⋊8S3 = C6×C33⋊C2φ: S3/C3 → C2 ⊆ Aut C32×C6108(C3^2xC6):8S3324,174
(C32×C6)⋊9S3 = C2×C34⋊C2φ: S3/C3 → C2 ⊆ Aut C32×C6162(C3^2xC6):9S3324,175

Non-split extensions G=N.Q with N=C32×C6 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C32×C6).1S3 = C32⋊Dic9φ: S3/C1 → S3 ⊆ Aut C32×C6108(C3^2xC6).1S3324,8
(C32×C6).2S3 = He3⋊C12φ: S3/C1 → S3 ⊆ Aut C32×C6363(C3^2xC6).2S3324,13
(C32×C6).3S3 = C32⋊2Dic9φ: S3/C1 → S3 ⊆ Aut C32×C6366(C3^2xC6).3S3324,20
(C32×C6).4S3 = C33⋊Dic3φ: S3/C1 → S3 ⊆ Aut C32×C6366-(C3^2xC6).4S3324,22
(C32×C6).5S3 = C2×C32⋊D9φ: S3/C1 → S3 ⊆ Aut C32×C654(C3^2xC6).5S3324,63
(C32×C6).6S3 = C2×C32⋊2D9φ: S3/C1 → S3 ⊆ Aut C32×C6366(C3^2xC6).6S3324,75
(C32×C6).7S3 = C3×C32⋊C12φ: S3/C1 → S3 ⊆ Aut C32×C6366(C3^2xC6).7S3324,92
(C32×C6).8S3 = C3×C9⋊C12φ: S3/C1 → S3 ⊆ Aut C32×C6366(C3^2xC6).8S3324,94
(C32×C6).9S3 = C33⋊4C12φ: S3/C1 → S3 ⊆ Aut C32×C6108(C3^2xC6).9S3324,98
(C32×C6).10S3 = C3×He3⋊3C4φ: S3/C1 → S3 ⊆ Aut C32×C6108(C3^2xC6).10S3324,99
(C32×C6).11S3 = C33.Dic3φ: S3/C1 → S3 ⊆ Aut C32×C6108(C3^2xC6).11S3324,100
(C32×C6).12S3 = He3⋊6Dic3φ: S3/C1 → S3 ⊆ Aut C32×C6366(C3^2xC6).12S3324,104
(C32×C6).13S3 = C6×C9⋊C6φ: S3/C1 → S3 ⊆ Aut C32×C6366(C3^2xC6).13S3324,140
(C32×C6).14S3 = C2×C33.S3φ: S3/C1 → S3 ⊆ Aut C32×C654(C3^2xC6).14S3324,146
(C32×C6).15S3 = C32×Dic9φ: S3/C3 → C2 ⊆ Aut C32×C6108(C3^2xC6).15S3324,90
(C32×C6).16S3 = C3×C9⋊Dic3φ: S3/C3 → C2 ⊆ Aut C32×C6108(C3^2xC6).16S3324,96
(C32×C6).17S3 = C32⋊5Dic9φ: S3/C3 → C2 ⊆ Aut C32×C6324(C3^2xC6).17S3324,103
(C32×C6).18S3 = D9×C3×C6φ: S3/C3 → C2 ⊆ Aut C32×C6108(C3^2xC6).18S3324,136
(C32×C6).19S3 = C6×C9⋊S3φ: S3/C3 → C2 ⊆ Aut C32×C6108(C3^2xC6).19S3324,142
(C32×C6).20S3 = C2×C32⋊4D9φ: S3/C3 → C2 ⊆ Aut C32×C6162(C3^2xC6).20S3324,149
(C32×C6).21S3 = C32×C3⋊Dic3φ: S3/C3 → C2 ⊆ Aut C32×C636(C3^2xC6).21S3324,156
(C32×C6).22S3 = C3×C33⋊5C4φ: S3/C3 → C2 ⊆ Aut C32×C6108(C3^2xC6).22S3324,157
(C32×C6).23S3 = C34⋊8C4φ: S3/C3 → C2 ⊆ Aut C32×C6324(C3^2xC6).23S3324,158
(C32×C6).24S3 = Dic3×C33central extension (φ=1)108(C3^2xC6).24S3324,155

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