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Extensions 1→N→G→Q→1 with N=C3xHe3 and Q=S3

Direct product G=NxQ with N=C3xHe3 and Q=S3
dρLabelID
C3xS3xHe354C3xS3xHe3486,223

Semidirect products G=N:Q with N=C3xHe3 and Q=S3
extensionφ:Q→Out NdρLabelID
(C3xHe3):1S3 = C3.C3wrS3φ: S3/C1 → S3 ⊆ Out C3xHe3546(C3xHe3):1S3486,4
(C3xHe3):2S3 = (C3xHe3):S3φ: S3/C1 → S3 ⊆ Out C3xHe381(C3xHe3):2S3486,43
(C3xHe3):3S3 = C34:C6φ: S3/C1 → S3 ⊆ Out C3xHe3186(C3xHe3):3S3486,102
(C3xHe3):4S3 = C3xC33:C6φ: S3/C1 → S3 ⊆ Out C3xHe3186(C3xHe3):4S3486,116
(C3xHe3):5S3 = C3wrC3:C6φ: S3/C1 → S3 ⊆ Out C3xHe3279(C3xHe3):5S3486,126
(C3xHe3):6S3 = (C3xHe3):C6φ: S3/C1 → S3 ⊆ Out C3xHe32718+(C3xHe3):6S3486,127
(C3xHe3):7S3 = C34:3S3φ: S3/C1 → S3 ⊆ Out C3xHe3186(C3xHe3):7S3486,145
(C3xHe3):8S3 = C34:4C6φ: S3/C1 → S3 ⊆ Out C3xHe327(C3xHe3):8S3486,146
(C3xHe3):9S3 = C3xC33:S3φ: S3/C1 → S3 ⊆ Out C3xHe3186(C3xHe3):9S3486,165
(C3xHe3):10S3 = C34:5C6φ: S3/C1 → S3 ⊆ Out C3xHe327(C3xHe3):10S3486,167
(C3xHe3):11S3 = C3xHe3:S3φ: S3/C1 → S3 ⊆ Out C3xHe3546(C3xHe3):11S3486,171
(C3xHe3):12S3 = C33:(C3xS3)φ: S3/C1 → S3 ⊆ Out C3xHe32718+(C3xHe3):12S3486,176
(C3xHe3):13S3 = He3:(C3xS3)φ: S3/C1 → S3 ⊆ Out C3xHe32718+(C3xHe3):13S3486,178
(C3xHe3):14S3 = C34:6S3φ: S3/C1 → S3 ⊆ Out C3xHe327(C3xHe3):14S3486,183
(C3xHe3):15S3 = C34:7S3φ: S3/C1 → S3 ⊆ Out C3xHe327(C3xHe3):15S3486,185
(C3xHe3):16S3 = C3:(He3:S3)φ: S3/C1 → S3 ⊆ Out C3xHe381(C3xHe3):16S3486,187
(C3xHe3):17S3 = 3+ 1+4:C2φ: S3/C1 → S3 ⊆ Out C3xHe32718+(C3xHe3):17S3486,236
(C3xHe3):18S3 = 3+ 1+4:2C2φ: S3/C1 → S3 ⊆ Out C3xHe3279(C3xHe3):18S3486,237
(C3xHe3):19S3 = 3+ 1+4:3C2φ: S3/C1 → S3 ⊆ Out C3xHe3279(C3xHe3):19S3486,249
(C3xHe3):20S3 = C3xHe3:4S3φ: S3/C3 → C2 ⊆ Out C3xHe354(C3xHe3):20S3486,229
(C3xHe3):21S3 = C3:S3xHe3φ: S3/C3 → C2 ⊆ Out C3xHe354(C3xHe3):21S3486,231
(C3xHe3):22S3 = C34:10C6φ: S3/C3 → C2 ⊆ Out C3xHe381(C3xHe3):22S3486,242
(C3xHe3):23S3 = C3xHe3:5S3φ: S3/C3 → C2 ⊆ Out C3xHe354(C3xHe3):23S3486,243
(C3xHe3):24S3 = C34:13S3φ: S3/C3 → C2 ⊆ Out C3xHe354(C3xHe3):24S3486,248

Non-split extensions G=N.Q with N=C3xHe3 and Q=S3
extensionφ:Q→Out NdρLabelID
(C3xHe3).1S3 = C32:C9:C6φ: S3/C1 → S3 ⊆ Out C3xHe3186(C3xHe3).1S3486,6
(C3xHe3).2S3 = C3.3C3wrS3φ: S3/C1 → S3 ⊆ Out C3xHe3546(C3xHe3).2S3486,8
(C3xHe3).3S3 = He3:D9φ: S3/C1 → S3 ⊆ Out C3xHe381(C3xHe3).3S3486,25
(C3xHe3).4S3 = (C3xHe3).S3φ: S3/C1 → S3 ⊆ Out C3xHe381(C3xHe3).4S3486,44
(C3xHe3).5S3 = C32:C9:6S3φ: S3/C1 → S3 ⊆ Out C3xHe381(C3xHe3).5S3486,46
(C3xHe3).6S3 = He3:2D9φ: S3/C1 → S3 ⊆ Out C3xHe381(C3xHe3).6S3486,56
(C3xHe3).7S3 = D9:He3φ: S3/C1 → S3 ⊆ Out C3xHe3546(C3xHe3).7S3486,106
(C3xHe3).8S3 = C3xHe3.S3φ: S3/C1 → S3 ⊆ Out C3xHe3546(C3xHe3).8S3486,119
(C3xHe3).9S3 = C3xHe3.2S3φ: S3/C1 → S3 ⊆ Out C3xHe3546(C3xHe3).9S3486,122
(C3xHe3).10S3 = C9:S3:C32φ: S3/C1 → S3 ⊆ Out C3xHe32718+(C3xHe3).10S3486,129
(C3xHe3).11S3 = He3.(C3xS3)φ: S3/C1 → S3 ⊆ Out C3xHe32718+(C3xHe3).11S3486,131
(C3xHe3).12S3 = C9:He3:2C2φ: S3/C1 → S3 ⊆ Out C3xHe381(C3xHe3).12S3486,148
(C3xHe3).13S3 = (C32xC9):S3φ: S3/C1 → S3 ⊆ Out C3xHe3546(C3xHe3).13S3486,149
(C3xHe3).14S3 = (C32xC9):C6φ: S3/C1 → S3 ⊆ Out C3xHe381(C3xHe3).14S3486,151
(C3xHe3).15S3 = C3xHe3.3S3φ: S3/C1 → S3 ⊆ Out C3xHe3546(C3xHe3).15S3486,168
(C3xHe3).16S3 = C32:4D9:C3φ: S3/C1 → S3 ⊆ Out C3xHe381(C3xHe3).16S3486,170
(C3xHe3).17S3 = He3:C3:3S3φ: S3/C1 → S3 ⊆ Out C3xHe381(C3xHe3).17S3486,173
(C3xHe3).18S3 = He3.C3:2C6φ: S3/C1 → S3 ⊆ Out C3xHe32718+(C3xHe3).18S3486,177
(C3xHe3).19S3 = He3.(C3:S3)φ: S3/C1 → S3 ⊆ Out C3xHe381(C3xHe3).19S3486,186
(C3xHe3).20S3 = 3- 1+4:C2φ: S3/C1 → S3 ⊆ Out C3xHe32718+(C3xHe3).20S3486,238
(C3xHe3).21S3 = D9xHe3φ: S3/C3 → C2 ⊆ Out C3xHe3546(C3xHe3).21S3486,99
(C3xHe3).22S3 = He3:3D9φ: S3/C3 → C2 ⊆ Out C3xHe381(C3xHe3).22S3486,142
(C3xHe3).23S3 = He3:4D9φ: S3/C3 → C2 ⊆ Out C3xHe3546(C3xHe3).23S3486,182
(C3xHe3).24S3 = C3xHe3.4S3φ: S3/C3 → C2 ⊆ Out C3xHe3546(C3xHe3).24S3486,234
(C3xHe3).25S3 = C9oHe3:3S3φ: S3/C3 → C2 ⊆ Out C3xHe381(C3xHe3).25S3486,245

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