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Extensions 1→N→G→Q→1 with N=C6×C12 and Q=S3

Direct product G=N×Q with N=C6×C12 and Q=S3
dρLabelID
S3×C6×C12144S3xC6xC12432,701

Semidirect products G=N:Q with N=C6×C12 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C6×C12)⋊1S3 = C62.21D6φ: S3/C1 → S3 ⊆ Aut C6×C1272(C6xC12):1S3432,141
(C6×C12)⋊2S3 = C62.31D6φ: S3/C1 → S3 ⊆ Aut C6×C1272(C6xC12):2S3432,189
(C6×C12)⋊3S3 = C62.36D6φ: S3/C1 → S3 ⊆ Aut C6×C12726(C6xC12):3S3432,351
(C6×C12)⋊4S3 = C62.47D6φ: S3/C1 → S3 ⊆ Aut C6×C12726(C6xC12):4S3432,387
(C6×C12)⋊5S3 = C2×He3⋊4D4φ: S3/C1 → S3 ⊆ Aut C6×C1272(C6xC12):5S3432,350
(C6×C12)⋊6S3 = C2×He3⋊5D4φ: S3/C1 → S3 ⊆ Aut C6×C1272(C6xC12):6S3432,386
(C6×C12)⋊7S3 = C2×C4×C32⋊C6φ: S3/C1 → S3 ⊆ Aut C6×C1272(C6xC12):7S3432,349
(C6×C12)⋊8S3 = C2×C4×He3⋊C2φ: S3/C1 → S3 ⊆ Aut C6×C1272(C6xC12):8S3432,385
(C6×C12)⋊9S3 = C32×D6⋊C4φ: S3/C3 → C2 ⊆ Aut C6×C12144(C6xC12):9S3432,474
(C6×C12)⋊10S3 = C3×C6.11D12φ: S3/C3 → C2 ⊆ Aut C6×C12144(C6xC12):10S3432,490
(C6×C12)⋊11S3 = C62.148D6φ: S3/C3 → C2 ⊆ Aut C6×C12216(C6xC12):11S3432,506
(C6×C12)⋊12S3 = C2×C33⋊12D4φ: S3/C3 → C2 ⊆ Aut C6×C12216(C6xC12):12S3432,722
(C6×C12)⋊13S3 = C62.160D6φ: S3/C3 → C2 ⊆ Aut C6×C12216(C6xC12):13S3432,723
(C6×C12)⋊14S3 = C3×C12.59D6φ: S3/C3 → C2 ⊆ Aut C6×C1272(C6xC12):14S3432,713
(C6×C12)⋊15S3 = C6×C12⋊S3φ: S3/C3 → C2 ⊆ Aut C6×C12144(C6xC12):15S3432,712
(C6×C12)⋊16S3 = C3⋊S3×C2×C12φ: S3/C3 → C2 ⊆ Aut C6×C12144(C6xC12):16S3432,711
(C6×C12)⋊17S3 = C2×C4×C33⋊C2φ: S3/C3 → C2 ⊆ Aut C6×C12216(C6xC12):17S3432,721
(C6×C12)⋊18S3 = C3×C6×D12φ: S3/C3 → C2 ⊆ Aut C6×C12144(C6xC12):18S3432,702
(C6×C12)⋊19S3 = C32×C4○D12φ: S3/C3 → C2 ⊆ Aut C6×C1272(C6xC12):19S3432,703

Non-split extensions G=N.Q with N=C6×C12 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C6×C12).1S3 = C62.19D6φ: S3/C1 → S3 ⊆ Aut C6×C12144(C6xC12).1S3432,139
(C6×C12).2S3 = Dic9⋊C12φ: S3/C1 → S3 ⊆ Aut C6×C12144(C6xC12).2S3432,145
(C6×C12).3S3 = D18⋊C12φ: S3/C1 → S3 ⊆ Aut C6×C1272(C6xC12).3S3432,147
(C6×C12).4S3 = C62.29D6φ: S3/C1 → S3 ⊆ Aut C6×C12144(C6xC12).4S3432,187
(C6×C12).5S3 = He3⋊7M4(2)φ: S3/C1 → S3 ⊆ Aut C6×C12726(C6xC12).5S3432,137
(C6×C12).6S3 = C36.C12φ: S3/C1 → S3 ⊆ Aut C6×C12726(C6xC12).6S3432,143
(C6×C12).7S3 = He3⋊8M4(2)φ: S3/C1 → S3 ⊆ Aut C6×C12726(C6xC12).7S3432,185
(C6×C12).8S3 = D36⋊6C6φ: S3/C1 → S3 ⊆ Aut C6×C12726(C6xC12).8S3432,355
(C6×C12).9S3 = C62.20D6φ: S3/C1 → S3 ⊆ Aut C6×C12144(C6xC12).9S3432,140
(C6×C12).10S3 = C36⋊C12φ: S3/C1 → S3 ⊆ Aut C6×C12144(C6xC12).10S3432,146
(C6×C12).11S3 = C62.30D6φ: S3/C1 → S3 ⊆ Aut C6×C12144(C6xC12).11S3432,188
(C6×C12).12S3 = C2×He3⋊3Q8φ: S3/C1 → S3 ⊆ Aut C6×C12144(C6xC12).12S3432,348
(C6×C12).13S3 = C2×C36.C6φ: S3/C1 → S3 ⊆ Aut C6×C12144(C6xC12).13S3432,352
(C6×C12).14S3 = C2×D36⋊C3φ: S3/C1 → S3 ⊆ Aut C6×C1272(C6xC12).14S3432,354
(C6×C12).15S3 = C2×He3⋊4Q8φ: S3/C1 → S3 ⊆ Aut C6×C12144(C6xC12).15S3432,384
(C6×C12).16S3 = C2×He3⋊3C8φ: S3/C1 → S3 ⊆ Aut C6×C12144(C6xC12).16S3432,136
(C6×C12).17S3 = C4×C32⋊C12φ: S3/C1 → S3 ⊆ Aut C6×C12144(C6xC12).17S3432,138
(C6×C12).18S3 = C2×C9⋊C24φ: S3/C1 → S3 ⊆ Aut C6×C12144(C6xC12).18S3432,142
(C6×C12).19S3 = C4×C9⋊C12φ: S3/C1 → S3 ⊆ Aut C6×C12144(C6xC12).19S3432,144
(C6×C12).20S3 = C2×He3⋊4C8φ: S3/C1 → S3 ⊆ Aut C6×C12144(C6xC12).20S3432,184
(C6×C12).21S3 = C4×He3⋊3C4φ: S3/C1 → S3 ⊆ Aut C6×C12144(C6xC12).21S3432,186
(C6×C12).22S3 = C2×C4×C9⋊C6φ: S3/C1 → S3 ⊆ Aut C6×C1272(C6xC12).22S3432,353
(C6×C12).23S3 = C3×Dic9⋊C4φ: S3/C3 → C2 ⊆ Aut C6×C12144(C6xC12).23S3432,129
(C6×C12).24S3 = C3×D18⋊C4φ: S3/C3 → C2 ⊆ Aut C6×C12144(C6xC12).24S3432,134
(C6×C12).25S3 = C6.Dic18φ: S3/C3 → C2 ⊆ Aut C6×C12432(C6xC12).25S3432,181
(C6×C12).26S3 = C6.11D36φ: S3/C3 → C2 ⊆ Aut C6×C12216(C6xC12).26S3432,183
(C6×C12).27S3 = C32×Dic3⋊C4φ: S3/C3 → C2 ⊆ Aut C6×C12144(C6xC12).27S3432,472
(C6×C12).28S3 = C3×C6.Dic6φ: S3/C3 → C2 ⊆ Aut C6×C12144(C6xC12).28S3432,488
(C6×C12).29S3 = C62.146D6φ: S3/C3 → C2 ⊆ Aut C6×C12432(C6xC12).29S3432,504
(C6×C12).30S3 = C36⋊Dic3φ: S3/C3 → C2 ⊆ Aut C6×C12432(C6xC12).30S3432,182
(C6×C12).31S3 = C2×C12.D9φ: S3/C3 → C2 ⊆ Aut C6×C12432(C6xC12).31S3432,380
(C6×C12).32S3 = C2×C36⋊S3φ: S3/C3 → C2 ⊆ Aut C6×C12216(C6xC12).32S3432,382
(C6×C12).33S3 = C62.147D6φ: S3/C3 → C2 ⊆ Aut C6×C12432(C6xC12).33S3432,505
(C6×C12).34S3 = C2×C33⋊8Q8φ: S3/C3 → C2 ⊆ Aut C6×C12432(C6xC12).34S3432,720
(C6×C12).35S3 = C36.69D6φ: S3/C3 → C2 ⊆ Aut C6×C12216(C6xC12).35S3432,179
(C6×C12).36S3 = C36.70D6φ: S3/C3 → C2 ⊆ Aut C6×C12216(C6xC12).36S3432,383
(C6×C12).37S3 = C33⋊18M4(2)φ: S3/C3 → C2 ⊆ Aut C6×C12216(C6xC12).37S3432,502
(C6×C12).38S3 = C3×C4.Dic9φ: S3/C3 → C2 ⊆ Aut C6×C12722(C6xC12).38S3432,125
(C6×C12).39S3 = C3×D36⋊5C2φ: S3/C3 → C2 ⊆ Aut C6×C12722(C6xC12).39S3432,344
(C6×C12).40S3 = C3×C12.58D6φ: S3/C3 → C2 ⊆ Aut C6×C1272(C6xC12).40S3432,486
(C6×C12).41S3 = C3×C4⋊Dic9φ: S3/C3 → C2 ⊆ Aut C6×C12144(C6xC12).41S3432,130
(C6×C12).42S3 = C6×Dic18φ: S3/C3 → C2 ⊆ Aut C6×C12144(C6xC12).42S3432,340
(C6×C12).43S3 = C6×D36φ: S3/C3 → C2 ⊆ Aut C6×C12144(C6xC12).43S3432,343
(C6×C12).44S3 = C3×C12⋊Dic3φ: S3/C3 → C2 ⊆ Aut C6×C12144(C6xC12).44S3432,489
(C6×C12).45S3 = C6×C32⋊4Q8φ: S3/C3 → C2 ⊆ Aut C6×C12144(C6xC12).45S3432,710
(C6×C12).46S3 = C6×C9⋊C8φ: S3/C3 → C2 ⊆ Aut C6×C12144(C6xC12).46S3432,124
(C6×C12).47S3 = C12×Dic9φ: S3/C3 → C2 ⊆ Aut C6×C12144(C6xC12).47S3432,128
(C6×C12).48S3 = C2×C36.S3φ: S3/C3 → C2 ⊆ Aut C6×C12432(C6xC12).48S3432,178
(C6×C12).49S3 = C4×C9⋊Dic3φ: S3/C3 → C2 ⊆ Aut C6×C12432(C6xC12).49S3432,180
(C6×C12).50S3 = D9×C2×C12φ: S3/C3 → C2 ⊆ Aut C6×C12144(C6xC12).50S3432,342
(C6×C12).51S3 = C2×C4×C9⋊S3φ: S3/C3 → C2 ⊆ Aut C6×C12216(C6xC12).51S3432,381
(C6×C12).52S3 = C6×C32⋊4C8φ: S3/C3 → C2 ⊆ Aut C6×C12144(C6xC12).52S3432,485
(C6×C12).53S3 = C12×C3⋊Dic3φ: S3/C3 → C2 ⊆ Aut C6×C12144(C6xC12).53S3432,487
(C6×C12).54S3 = C2×C33⋊7C8φ: S3/C3 → C2 ⊆ Aut C6×C12432(C6xC12).54S3432,501
(C6×C12).55S3 = C4×C33⋊5C4φ: S3/C3 → C2 ⊆ Aut C6×C12432(C6xC12).55S3432,503
(C6×C12).56S3 = C32×C4.Dic3φ: S3/C3 → C2 ⊆ Aut C6×C1272(C6xC12).56S3432,470
(C6×C12).57S3 = C32×C4⋊Dic3φ: S3/C3 → C2 ⊆ Aut C6×C12144(C6xC12).57S3432,473
(C6×C12).58S3 = C3×C6×Dic6φ: S3/C3 → C2 ⊆ Aut C6×C12144(C6xC12).58S3432,700
(C6×C12).59S3 = C3×C6×C3⋊C8central extension (φ=1)144(C6xC12).59S3432,469
(C6×C12).60S3 = Dic3×C3×C12central extension (φ=1)144(C6xC12).60S3432,471

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