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Extensions 1→N→G→Q→1 with N=C3×He3 and Q=S3

Direct product G=N×Q with N=C3×He3 and Q=S3
dρLabelID
C3×S3×He354C3xS3xHe3486,223

Semidirect products G=N:Q with N=C3×He3 and Q=S3
extensionφ:Q→Out NdρLabelID
(C3×He3)⋊1S3 = C3.C3≀S3φ: S3/C1 → S3 ⊆ Out C3×He3546(C3xHe3):1S3486,4
(C3×He3)⋊2S3 = (C3×He3)⋊S3φ: S3/C1 → S3 ⊆ Out C3×He381(C3xHe3):2S3486,43
(C3×He3)⋊3S3 = C34⋊C6φ: S3/C1 → S3 ⊆ Out C3×He3186(C3xHe3):3S3486,102
(C3×He3)⋊4S3 = C3×C33⋊C6φ: S3/C1 → S3 ⊆ Out C3×He3186(C3xHe3):4S3486,116
(C3×He3)⋊5S3 = C3≀C3⋊C6φ: S3/C1 → S3 ⊆ Out C3×He3279(C3xHe3):5S3486,126
(C3×He3)⋊6S3 = (C3×He3)⋊C6φ: S3/C1 → S3 ⊆ Out C3×He32718+(C3xHe3):6S3486,127
(C3×He3)⋊7S3 = C34⋊3S3φ: S3/C1 → S3 ⊆ Out C3×He3186(C3xHe3):7S3486,145
(C3×He3)⋊8S3 = C34⋊4C6φ: S3/C1 → S3 ⊆ Out C3×He327(C3xHe3):8S3486,146
(C3×He3)⋊9S3 = C3×C33⋊S3φ: S3/C1 → S3 ⊆ Out C3×He3186(C3xHe3):9S3486,165
(C3×He3)⋊10S3 = C34⋊5C6φ: S3/C1 → S3 ⊆ Out C3×He327(C3xHe3):10S3486,167
(C3×He3)⋊11S3 = C3×He3⋊S3φ: S3/C1 → S3 ⊆ Out C3×He3546(C3xHe3):11S3486,171
(C3×He3)⋊12S3 = C33⋊(C3×S3)φ: S3/C1 → S3 ⊆ Out C3×He32718+(C3xHe3):12S3486,176
(C3×He3)⋊13S3 = He3⋊(C3×S3)φ: S3/C1 → S3 ⊆ Out C3×He32718+(C3xHe3):13S3486,178
(C3×He3)⋊14S3 = C34⋊6S3φ: S3/C1 → S3 ⊆ Out C3×He327(C3xHe3):14S3486,183
(C3×He3)⋊15S3 = C34⋊7S3φ: S3/C1 → S3 ⊆ Out C3×He327(C3xHe3):15S3486,185
(C3×He3)⋊16S3 = C3⋊(He3⋊S3)φ: S3/C1 → S3 ⊆ Out C3×He381(C3xHe3):16S3486,187
(C3×He3)⋊17S3 = 3+ 1+4⋊C2φ: S3/C1 → S3 ⊆ Out C3×He32718+(C3xHe3):17S3486,236
(C3×He3)⋊18S3 = 3+ 1+4⋊2C2φ: S3/C1 → S3 ⊆ Out C3×He3279(C3xHe3):18S3486,237
(C3×He3)⋊19S3 = 3+ 1+4⋊3C2φ: S3/C1 → S3 ⊆ Out C3×He3279(C3xHe3):19S3486,249
(C3×He3)⋊20S3 = C3×He3⋊4S3φ: S3/C3 → C2 ⊆ Out C3×He354(C3xHe3):20S3486,229
(C3×He3)⋊21S3 = C3⋊S3×He3φ: S3/C3 → C2 ⊆ Out C3×He354(C3xHe3):21S3486,231
(C3×He3)⋊22S3 = C34⋊10C6φ: S3/C3 → C2 ⊆ Out C3×He381(C3xHe3):22S3486,242
(C3×He3)⋊23S3 = C3×He3⋊5S3φ: S3/C3 → C2 ⊆ Out C3×He354(C3xHe3):23S3486,243
(C3×He3)⋊24S3 = C34⋊13S3φ: S3/C3 → C2 ⊆ Out C3×He354(C3xHe3):24S3486,248

Non-split extensions G=N.Q with N=C3×He3 and Q=S3
extensionφ:Q→Out NdρLabelID
(C3×He3).1S3 = C32⋊C9⋊C6φ: S3/C1 → S3 ⊆ Out C3×He3186(C3xHe3).1S3486,6
(C3×He3).2S3 = C3.3C3≀S3φ: S3/C1 → S3 ⊆ Out C3×He3546(C3xHe3).2S3486,8
(C3×He3).3S3 = He3⋊D9φ: S3/C1 → S3 ⊆ Out C3×He381(C3xHe3).3S3486,25
(C3×He3).4S3 = (C3×He3).S3φ: S3/C1 → S3 ⊆ Out C3×He381(C3xHe3).4S3486,44
(C3×He3).5S3 = C32⋊C9⋊6S3φ: S3/C1 → S3 ⊆ Out C3×He381(C3xHe3).5S3486,46
(C3×He3).6S3 = He3⋊2D9φ: S3/C1 → S3 ⊆ Out C3×He381(C3xHe3).6S3486,56
(C3×He3).7S3 = D9⋊He3φ: S3/C1 → S3 ⊆ Out C3×He3546(C3xHe3).7S3486,106
(C3×He3).8S3 = C3×He3.S3φ: S3/C1 → S3 ⊆ Out C3×He3546(C3xHe3).8S3486,119
(C3×He3).9S3 = C3×He3.2S3φ: S3/C1 → S3 ⊆ Out C3×He3546(C3xHe3).9S3486,122
(C3×He3).10S3 = C9⋊S3⋊C32φ: S3/C1 → S3 ⊆ Out C3×He32718+(C3xHe3).10S3486,129
(C3×He3).11S3 = He3.(C3×S3)φ: S3/C1 → S3 ⊆ Out C3×He32718+(C3xHe3).11S3486,131
(C3×He3).12S3 = C9⋊He3⋊2C2φ: S3/C1 → S3 ⊆ Out C3×He381(C3xHe3).12S3486,148
(C3×He3).13S3 = (C32×C9)⋊S3φ: S3/C1 → S3 ⊆ Out C3×He3546(C3xHe3).13S3486,149
(C3×He3).14S3 = (C32×C9)⋊C6φ: S3/C1 → S3 ⊆ Out C3×He381(C3xHe3).14S3486,151
(C3×He3).15S3 = C3×He3.3S3φ: S3/C1 → S3 ⊆ Out C3×He3546(C3xHe3).15S3486,168
(C3×He3).16S3 = C32⋊4D9⋊C3φ: S3/C1 → S3 ⊆ Out C3×He381(C3xHe3).16S3486,170
(C3×He3).17S3 = He3⋊C3⋊3S3φ: S3/C1 → S3 ⊆ Out C3×He381(C3xHe3).17S3486,173
(C3×He3).18S3 = He3.C3⋊2C6φ: S3/C1 → S3 ⊆ Out C3×He32718+(C3xHe3).18S3486,177
(C3×He3).19S3 = He3.(C3⋊S3)φ: S3/C1 → S3 ⊆ Out C3×He381(C3xHe3).19S3486,186
(C3×He3).20S3 = 3- 1+4⋊C2φ: S3/C1 → S3 ⊆ Out C3×He32718+(C3xHe3).20S3486,238
(C3×He3).21S3 = D9×He3φ: S3/C3 → C2 ⊆ Out C3×He3546(C3xHe3).21S3486,99
(C3×He3).22S3 = He3⋊3D9φ: S3/C3 → C2 ⊆ Out C3×He381(C3xHe3).22S3486,142
(C3×He3).23S3 = He3⋊4D9φ: S3/C3 → C2 ⊆ Out C3×He3546(C3xHe3).23S3486,182
(C3×He3).24S3 = C3×He3.4S3φ: S3/C3 → C2 ⊆ Out C3×He3546(C3xHe3).24S3486,234
(C3×He3).25S3 = C9○He3⋊3S3φ: S3/C3 → C2 ⊆ Out C3×He381(C3xHe3).25S3486,245

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