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

Direct product G=N×Q with N=C6×C12 and Q=C6
dρLabelID
C62×C12432C6^2xC12432,730

Semidirect products G=N:Q with N=C6×C12 and Q=C6
extensionφ:Q→Aut NdρLabelID
(C6×C12)⋊1C6 = C62.21D6φ: C6/C1 → C6 ⊆ Aut C6×C1272(C6xC12):1C6432,141
(C6×C12)⋊2C6 = C22⋊C4×He3φ: C6/C1 → C6 ⊆ Aut C6×C1272(C6xC12):2C6432,204
(C6×C12)⋊3C6 = C2×He3⋊4D4φ: C6/C1 → C6 ⊆ Aut C6×C1272(C6xC12):3C6432,350
(C6×C12)⋊4C6 = C62.36D6φ: C6/C1 → C6 ⊆ Aut C6×C12726(C6xC12):4C6432,351
(C6×C12)⋊5C6 = C2×C4×C32⋊C6φ: C6/C1 → C6 ⊆ Aut C6×C1272(C6xC12):5C6432,349
(C6×C12)⋊6C6 = C2×D4×He3φ: C6/C1 → C6 ⊆ Aut C6×C1272(C6xC12):6C6432,404
(C6×C12)⋊7C6 = C4○D4×He3φ: C6/C1 → C6 ⊆ Aut C6×C12726(C6xC12):7C6432,410
(C6×C12)⋊8C6 = C22×C4×He3φ: C6/C2 → C3 ⊆ Aut C6×C12144(C6xC12):8C6432,401
(C6×C12)⋊9C6 = C32×D6⋊C4φ: C6/C3 → C2 ⊆ Aut C6×C12144(C6xC12):9C6432,474
(C6×C12)⋊10C6 = C3×C6.11D12φ: C6/C3 → C2 ⊆ Aut C6×C12144(C6xC12):10C6432,490
(C6×C12)⋊11C6 = C22⋊C4×C33φ: C6/C3 → C2 ⊆ Aut C6×C12216(C6xC12):11C6432,513
(C6×C12)⋊12C6 = C6×C12⋊S3φ: C6/C3 → C2 ⊆ Aut C6×C12144(C6xC12):12C6432,712
(C6×C12)⋊13C6 = C3×C12.59D6φ: C6/C3 → C2 ⊆ Aut C6×C1272(C6xC12):13C6432,713
(C6×C12)⋊14C6 = C32×C4○D12φ: C6/C3 → C2 ⊆ Aut C6×C1272(C6xC12):14C6432,703
(C6×C12)⋊15C6 = C3×C6×D12φ: C6/C3 → C2 ⊆ Aut C6×C12144(C6xC12):15C6432,702
(C6×C12)⋊16C6 = S3×C6×C12φ: C6/C3 → C2 ⊆ Aut C6×C12144(C6xC12):16C6432,701
(C6×C12)⋊17C6 = C3⋊S3×C2×C12φ: C6/C3 → C2 ⊆ Aut C6×C12144(C6xC12):17C6432,711
(C6×C12)⋊18C6 = D4×C32×C6φ: C6/C3 → C2 ⊆ Aut C6×C12216(C6xC12):18C6432,731
(C6×C12)⋊19C6 = C4○D4×C33φ: C6/C3 → C2 ⊆ Aut C6×C12216(C6xC12):19C6432,733

Non-split extensions G=N.Q with N=C6×C12 and Q=C6
extensionφ:Q→Aut NdρLabelID
(C6×C12).1C6 = C62.19D6φ: C6/C1 → C6 ⊆ Aut C6×C12144(C6xC12).1C6432,139
(C6×C12).2C6 = C22⋊C4×3- 1+2φ: C6/C1 → C6 ⊆ Aut C6×C1272(C6xC12).2C6432,205
(C6×C12).3C6 = C4⋊C4×He3φ: C6/C1 → C6 ⊆ Aut C6×C12144(C6xC12).3C6432,207
(C6×C12).4C6 = C4⋊C4×3- 1+2φ: C6/C1 → C6 ⊆ Aut C6×C12144(C6xC12).4C6432,208
(C6×C12).5C6 = C62.20D6φ: C6/C1 → C6 ⊆ Aut C6×C12144(C6xC12).5C6432,140
(C6×C12).6C6 = C2×He3⋊3Q8φ: C6/C1 → C6 ⊆ Aut C6×C12144(C6xC12).6C6432,348
(C6×C12).7C6 = He3⋊7M4(2)φ: C6/C1 → C6 ⊆ Aut C6×C12726(C6xC12).7C6432,137
(C6×C12).8C6 = C2×He3⋊3C8φ: C6/C1 → C6 ⊆ Aut C6×C12144(C6xC12).8C6432,136
(C6×C12).9C6 = C4×C32⋊C12φ: C6/C1 → C6 ⊆ Aut C6×C12144(C6xC12).9C6432,138
(C6×C12).10C6 = M4(2)×He3φ: C6/C1 → C6 ⊆ Aut C6×C12726(C6xC12).10C6432,213
(C6×C12).11C6 = M4(2)×3- 1+2φ: C6/C1 → C6 ⊆ Aut C6×C12726(C6xC12).11C6432,214
(C6×C12).12C6 = C2×D4×3- 1+2φ: C6/C1 → C6 ⊆ Aut C6×C1272(C6xC12).12C6432,405
(C6×C12).13C6 = C2×Q8×He3φ: C6/C1 → C6 ⊆ Aut C6×C12144(C6xC12).13C6432,407
(C6×C12).14C6 = C2×Q8×3- 1+2φ: C6/C1 → C6 ⊆ Aut C6×C12144(C6xC12).14C6432,408
(C6×C12).15C6 = C4○D4×3- 1+2φ: C6/C1 → C6 ⊆ Aut C6×C12726(C6xC12).15C6432,411
(C6×C12).16C6 = C42×He3φ: C6/C2 → C3 ⊆ Aut C6×C12144(C6xC12).16C6432,201
(C6×C12).17C6 = C42×3- 1+2φ: C6/C2 → C3 ⊆ Aut C6×C12144(C6xC12).17C6432,202
(C6×C12).18C6 = C2×C8×He3φ: C6/C2 → C3 ⊆ Aut C6×C12144(C6xC12).18C6432,210
(C6×C12).19C6 = C2×C8×3- 1+2φ: C6/C2 → C3 ⊆ Aut C6×C12144(C6xC12).19C6432,211
(C6×C12).20C6 = C22×C4×3- 1+2φ: C6/C2 → C3 ⊆ Aut C6×C12144(C6xC12).20C6432,402
(C6×C12).21C6 = C9×Dic3⋊C4φ: C6/C3 → C2 ⊆ Aut C6×C12144(C6xC12).21C6432,132
(C6×C12).22C6 = C9×D6⋊C4φ: C6/C3 → C2 ⊆ Aut C6×C12144(C6xC12).22C6432,135
(C6×C12).23C6 = C22⋊C4×C3×C9φ: C6/C3 → C2 ⊆ Aut C6×C12216(C6xC12).23C6432,203
(C6×C12).24C6 = C4⋊C4×C3×C9φ: C6/C3 → C2 ⊆ Aut C6×C12432(C6xC12).24C6432,206
(C6×C12).25C6 = C32×Dic3⋊C4φ: C6/C3 → C2 ⊆ Aut C6×C12144(C6xC12).25C6432,472
(C6×C12).26C6 = C3×C6.Dic6φ: C6/C3 → C2 ⊆ Aut C6×C12144(C6xC12).26C6432,488
(C6×C12).27C6 = C4⋊C4×C33φ: C6/C3 → C2 ⊆ Aut C6×C12432(C6xC12).27C6432,514
(C6×C12).28C6 = C3×C12⋊Dic3φ: C6/C3 → C2 ⊆ Aut C6×C12144(C6xC12).28C6432,489
(C6×C12).29C6 = C6×C32⋊4Q8φ: C6/C3 → C2 ⊆ Aut C6×C12144(C6xC12).29C6432,710
(C6×C12).30C6 = C3×C12.58D6φ: C6/C3 → C2 ⊆ Aut C6×C1272(C6xC12).30C6432,486
(C6×C12).31C6 = C9×C4.Dic3φ: C6/C3 → C2 ⊆ Aut C6×C12722(C6xC12).31C6432,127
(C6×C12).32C6 = C9×C4○D12φ: C6/C3 → C2 ⊆ Aut C6×C12722(C6xC12).32C6432,347
(C6×C12).33C6 = C32×C4.Dic3φ: C6/C3 → C2 ⊆ Aut C6×C1272(C6xC12).33C6432,470
(C6×C12).34C6 = C9×C4⋊Dic3φ: C6/C3 → C2 ⊆ Aut C6×C12144(C6xC12).34C6432,133
(C6×C12).35C6 = C18×Dic6φ: C6/C3 → C2 ⊆ Aut C6×C12144(C6xC12).35C6432,341
(C6×C12).36C6 = C18×D12φ: C6/C3 → C2 ⊆ Aut C6×C12144(C6xC12).36C6432,346
(C6×C12).37C6 = C32×C4⋊Dic3φ: C6/C3 → C2 ⊆ Aut C6×C12144(C6xC12).37C6432,473
(C6×C12).38C6 = C3×C6×Dic6φ: C6/C3 → C2 ⊆ Aut C6×C12144(C6xC12).38C6432,700
(C6×C12).39C6 = C18×C3⋊C8φ: C6/C3 → C2 ⊆ Aut C6×C12144(C6xC12).39C6432,126
(C6×C12).40C6 = Dic3×C36φ: C6/C3 → C2 ⊆ Aut C6×C12144(C6xC12).40C6432,131
(C6×C12).41C6 = S3×C2×C36φ: C6/C3 → C2 ⊆ Aut C6×C12144(C6xC12).41C6432,345
(C6×C12).42C6 = C3×C6×C3⋊C8φ: C6/C3 → C2 ⊆ Aut C6×C12144(C6xC12).42C6432,469
(C6×C12).43C6 = Dic3×C3×C12φ: C6/C3 → C2 ⊆ Aut C6×C12144(C6xC12).43C6432,471
(C6×C12).44C6 = C6×C32⋊4C8φ: C6/C3 → C2 ⊆ Aut C6×C12144(C6xC12).44C6432,485
(C6×C12).45C6 = C12×C3⋊Dic3φ: C6/C3 → C2 ⊆ Aut C6×C12144(C6xC12).45C6432,487
(C6×C12).46C6 = M4(2)×C3×C9φ: C6/C3 → C2 ⊆ Aut C6×C12216(C6xC12).46C6432,212
(C6×C12).47C6 = D4×C3×C18φ: C6/C3 → C2 ⊆ Aut C6×C12216(C6xC12).47C6432,403
(C6×C12).48C6 = Q8×C3×C18φ: C6/C3 → C2 ⊆ Aut C6×C12432(C6xC12).48C6432,406
(C6×C12).49C6 = C4○D4×C3×C9φ: C6/C3 → C2 ⊆ Aut C6×C12216(C6xC12).49C6432,409
(C6×C12).50C6 = M4(2)×C33φ: C6/C3 → C2 ⊆ Aut C6×C12216(C6xC12).50C6432,516
(C6×C12).51C6 = Q8×C32×C6φ: C6/C3 → C2 ⊆ Aut C6×C12432(C6xC12).51C6432,732

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