# Extensions 1→N→G→Q→1 with N=C32×C9 and Q=S3

Direct product G=N×Q with N=C32×C9 and Q=S3
dρLabelID
S3×C32×C9162S3xC3^2xC9486,221

Semidirect products G=N:Q with N=C32×C9 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C32×C9)⋊1S3 = He3⋊C18φ: S3/C1S3 ⊆ Aut C32×C981(C3^2xC9):1S3486,24
(C32×C9)⋊2S3 = C3×C32⋊C18φ: S3/C1S3 ⊆ Aut C32×C954(C3^2xC9):2S3486,93
(C32×C9)⋊3S3 = C9×C32⋊C6φ: S3/C1S3 ⊆ Aut C32×C9546(C3^2xC9):3S3486,98
(C32×C9)⋊4S3 = C3×He3.C6φ: S3/C1S3 ⊆ Aut C32×C981(C3^2xC9):4S3486,118
(C32×C9)⋊5S3 = C3×He3.2C6φ: S3/C1S3 ⊆ Aut C32×C981(C3^2xC9):5S3486,121
(C32×C9)⋊6S3 = C33⋊C18φ: S3/C1S3 ⊆ Aut C32×C954(C3^2xC9):6S3486,136
(C32×C9)⋊7S3 = C9×He3⋊C2φ: S3/C1S3 ⊆ Aut C32×C981(C3^2xC9):7S3486,143
(C32×C9)⋊8S3 = (C32×C9)⋊8S3φ: S3/C1S3 ⊆ Aut C32×C9546(C3^2xC9):8S3486,150
(C32×C9)⋊9S3 = He3.C3⋊S3φ: S3/C1S3 ⊆ Aut C32×C9546(C3^2xC9):9S3486,169
(C32×C9)⋊10S3 = He3⋊C32S3φ: S3/C1S3 ⊆ Aut C32×C9546(C3^2xC9):10S3486,172
(C32×C9)⋊11S3 = He32D9φ: S3/C1S3 ⊆ Aut C32×C981(C3^2xC9):11S3486,56
(C32×C9)⋊12S3 = C3×C322D9φ: S3/C1S3 ⊆ Aut C32×C954(C3^2xC9):12S3486,135
(C32×C9)⋊13S3 = He33D9φ: S3/C1S3 ⊆ Aut C32×C981(C3^2xC9):13S3486,142
(C32×C9)⋊14S3 = (C32×C9)⋊S3φ: S3/C1S3 ⊆ Aut C32×C9546(C3^2xC9):14S3486,149
(C32×C9)⋊15S3 = C3×He3.3S3φ: S3/C1S3 ⊆ Aut C32×C9546(C3^2xC9):15S3486,168
(C32×C9)⋊16S3 = C3×He3⋊S3φ: S3/C1S3 ⊆ Aut C32×C9546(C3^2xC9):16S3486,171
(C32×C9)⋊17S3 = C336D9φ: S3/C1S3 ⊆ Aut C32×C954(C3^2xC9):17S3486,181
(C32×C9)⋊18S3 = He34D9φ: S3/C1S3 ⊆ Aut C32×C9546(C3^2xC9):18S3486,182
(C32×C9)⋊19S3 = He3.(C3⋊S3)φ: S3/C1S3 ⊆ Aut C32×C981(C3^2xC9):19S3486,186
(C32×C9)⋊20S3 = C3⋊(He3⋊S3)φ: S3/C1S3 ⊆ Aut C32×C981(C3^2xC9):20S3486,187
(C32×C9)⋊21S3 = C3≀C3⋊S3φ: S3/C1S3 ⊆ Aut C32×C9276+(C3^2xC9):21S3486,189
(C32×C9)⋊22S3 = C3×He3.4S3φ: S3/C1S3 ⊆ Aut C32×C9546(C3^2xC9):22S3486,234
(C32×C9)⋊23S3 = C9○He33S3φ: S3/C1S3 ⊆ Aut C32×C981(C3^2xC9):23S3486,245
(C32×C9)⋊24S3 = C3≀S33C3φ: S3/C1S3 ⊆ Aut C32×C9273(C3^2xC9):24S3486,125
(C32×C9)⋊25S3 = C3×He3.4C6φ: S3/C1S3 ⊆ Aut C32×C981(C3^2xC9):25S3486,235
(C32×C9)⋊26S3 = C9○He34S3φ: S3/C1S3 ⊆ Aut C32×C9546(C3^2xC9):26S3486,246
(C32×C9)⋊27S3 = C3⋊S3×C3×C9φ: S3/C3C2 ⊆ Aut C32×C954(C3^2xC9):27S3486,228
(C32×C9)⋊28S3 = C9×C33⋊C2φ: S3/C3C2 ⊆ Aut C32×C9162(C3^2xC9):28S3486,241
(C32×C9)⋊29S3 = C32×C9⋊S3φ: S3/C3C2 ⊆ Aut C32×C954(C3^2xC9):29S3486,227
(C32×C9)⋊30S3 = C3×C324D9φ: S3/C3C2 ⊆ Aut C32×C9162(C3^2xC9):30S3486,240
(C32×C9)⋊31S3 = C339D9φ: S3/C3C2 ⊆ Aut C32×C9243(C3^2xC9):31S3486,247

Non-split extensions G=N.Q with N=C32×C9 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C32×C9).1S3 = C9⋊S3⋊C9φ: S3/C1S3 ⊆ Aut C32×C954(C3^2xC9).1S3486,3
(C32×C9).2S3 = (C3×C9)⋊D9φ: S3/C1S3 ⊆ Aut C32×C9546(C3^2xC9).2S3486,21
(C32×C9).3S3 = (C3×C9)⋊3D9φ: S3/C1S3 ⊆ Aut C32×C9546(C3^2xC9).3S3486,23
(C32×C9).4S3 = C3×C9⋊C18φ: S3/C1S3 ⊆ Aut C32×C954(C3^2xC9).4S3486,96
(C32×C9).5S3 = C9×C9⋊C6φ: S3/C1S3 ⊆ Aut C32×C9546(C3^2xC9).5S3486,100
(C32×C9).6S3 = C9⋊(S3×C9)φ: S3/C1S3 ⊆ Aut C32×C954(C3^2xC9).6S3486,138
(C32×C9).7S3 = C9⋊C92S3φ: S3/C1S3 ⊆ Aut C32×C9546(C3^2xC9).7S3486,152
(C32×C9).8S3 = C32⋊D27φ: S3/C1S3 ⊆ Aut C32×C981(C3^2xC9).8S3486,17
(C32×C9).9S3 = C3.2(C9⋊D9)φ: S3/C1S3 ⊆ Aut C32×C9162(C3^2xC9).9S3486,42
(C32×C9).10S3 = C322D27φ: S3/C1S3 ⊆ Aut C32×C9546(C3^2xC9).10S3486,51
(C32×C9).11S3 = (C3×C9)⋊5D9φ: S3/C1S3 ⊆ Aut C32×C981(C3^2xC9).11S3486,53
(C32×C9).12S3 = (C3×C9)⋊6D9φ: S3/C1S3 ⊆ Aut C32×C981(C3^2xC9).12S3486,54
(C32×C9).13S3 = 3- 1+2⋊D9φ: S3/C1S3 ⊆ Aut C32×C981(C3^2xC9).13S3486,57
(C32×C9).14S3 = C929C6φ: S3/C1S3 ⊆ Aut C32×C981(C3^2xC9).14S3486,144
(C32×C9).15S3 = C3×3- 1+2.S3φ: S3/C1S3 ⊆ Aut C32×C9546(C3^2xC9).15S3486,174
(C32×C9).16S3 = (C32×C9).S3φ: S3/C1S3 ⊆ Aut C32×C981(C3^2xC9).16S3486,188
(C32×C9).17S3 = C33.D9φ: S3/C1S3 ⊆ Aut C32×C9276+(C3^2xC9).17S3486,55
(C32×C9).18S3 = C3×C27⋊C6φ: S3/C1S3 ⊆ Aut C32×C9546(C3^2xC9).18S3486,113
(C32×C9).19S3 = C923C6φ: S3/C1S3 ⊆ Aut C32×C981(C3^2xC9).19S3486,141
(C32×C9).20S3 = C33.5D9φ: S3/C1S3 ⊆ Aut C32×C981(C3^2xC9).20S3486,162
(C32×C9).21S3 = C924S3φ: S3/C1S3 ⊆ Aut C32×C9546(C3^2xC9).21S3486,140
(C32×C9).22S3 = D9×C3×C9φ: S3/C3C2 ⊆ Aut C32×C954(C3^2xC9).22S3486,91
(C32×C9).23S3 = C9×C9⋊S3φ: S3/C3C2 ⊆ Aut C32×C954(C3^2xC9).23S3486,133
(C32×C9).24S3 = C32×D27φ: S3/C3C2 ⊆ Aut C32×C9162(C3^2xC9).24S3486,111
(C32×C9).25S3 = C3×C9⋊D9φ: S3/C3C2 ⊆ Aut C32×C9162(C3^2xC9).25S3486,134
(C32×C9).26S3 = C3×C27⋊S3φ: S3/C3C2 ⊆ Aut C32×C9162(C3^2xC9).26S3486,160
(C32×C9).27S3 = C928S3φ: S3/C3C2 ⊆ Aut C32×C9243(C3^2xC9).27S3486,180
(C32×C9).28S3 = C324D27φ: S3/C3C2 ⊆ Aut C32×C9243(C3^2xC9).28S3486,184

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