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Extensions 1→N→G→Q→1 with N=S3×C2×C4 and Q=C4

Direct product G=N×Q with N=S3×C2×C4 and Q=C4
dρLabelID
S3×C2×C4296S3xC2xC4^2192,1030

Semidirect products G=N:Q with N=S3×C2×C4 and Q=C4
extensionφ:Q→Out NdρLabelID
(S3×C2×C4)⋊1C4 = C23⋊C4⋊5S3φ: C4/C1 → C4 ⊆ Out S3×C2×C4488-(S3xC2xC4):1C4192,299
(S3×C2×C4)⋊2C4 = S3×C23⋊C4φ: C4/C1 → C4 ⊆ Out S3×C2×C4248+(S3xC2xC4):2C4192,302
(S3×C2×C4)⋊3C4 = (C2×D12)⋊13C4φ: C4/C1 → C4 ⊆ Out S3×C2×C4484(S3xC2xC4):3C4192,565
(S3×C2×C4)⋊4C4 = C4⋊(D6⋊C4)φ: C4/C2 → C2 ⊆ Out S3×C2×C496(S3xC2xC4):4C4192,546
(S3×C2×C4)⋊5C4 = C2×S3×C4⋊C4φ: C4/C2 → C2 ⊆ Out S3×C2×C496(S3xC2xC4):5C4192,1060
(S3×C2×C4)⋊6C4 = C2×C4⋊C4⋊7S3φ: C4/C2 → C2 ⊆ Out S3×C2×C496(S3xC2xC4):6C4192,1061
(S3×C2×C4)⋊7C4 = S3×C42⋊C2φ: C4/C2 → C2 ⊆ Out S3×C2×C448(S3xC2xC4):7C4192,1079
(S3×C2×C4)⋊8C4 = S3×C2.C42φ: C4/C2 → C2 ⊆ Out S3×C2×C496(S3xC2xC4):8C4192,222
(S3×C2×C4)⋊9C4 = C22.58(S3×D4)φ: C4/C2 → C2 ⊆ Out S3×C2×C496(S3xC2xC4):9C4192,223
(S3×C2×C4)⋊10C4 = D6⋊C42φ: C4/C2 → C2 ⊆ Out S3×C2×C496(S3xC2xC4):10C4192,225
(S3×C2×C4)⋊11C4 = D6⋊(C4⋊C4)φ: C4/C2 → C2 ⊆ Out S3×C2×C496(S3xC2xC4):11C4192,226
(S3×C2×C4)⋊12C4 = C4×D6⋊C4φ: C4/C2 → C2 ⊆ Out S3×C2×C496(S3xC2xC4):12C4192,497
(S3×C2×C4)⋊13C4 = C2×C42⋊2S3φ: C4/C2 → C2 ⊆ Out S3×C2×C496(S3xC2xC4):13C4192,1031

Non-split extensions G=N.Q with N=S3×C2×C4 and Q=C4
extensionφ:Q→Out NdρLabelID
(S3×C2×C4).1C4 = C8.25D12φ: C4/C1 → C4 ⊆ Out S3×C2×C4484(S3xC2xC4).1C4192,73
(S3×C2×C4).2C4 = S3×C4.10D4φ: C4/C1 → C4 ⊆ Out S3×C2×C4488-(S3xC2xC4).2C4192,309
(S3×C2×C4).3C4 = M4(2).21D6φ: C4/C1 → C4 ⊆ Out S3×C2×C4488+(S3xC2xC4).3C4192,310
(S3×C2×C4).4C4 = M4(2).31D6φ: C4/C1 → C4 ⊆ Out S3×C2×C4484(S3xC2xC4).4C4192,691
(S3×C2×C4).5C4 = S3×C4⋊C8φ: C4/C2 → C2 ⊆ Out S3×C2×C496(S3xC2xC4).5C4192,391
(S3×C2×C4).6C4 = C42.200D6φ: C4/C2 → C2 ⊆ Out S3×C2×C496(S3xC2xC4).6C4192,392
(S3×C2×C4).7C4 = C12⋊M4(2)φ: C4/C2 → C2 ⊆ Out S3×C2×C496(S3xC2xC4).7C4192,396
(S3×C2×C4).8C4 = S3×M5(2)φ: C4/C2 → C2 ⊆ Out S3×C2×C4484(S3xC2xC4).8C4192,465
(S3×C2×C4).9C4 = D6⋊6M4(2)φ: C4/C2 → C2 ⊆ Out S3×C2×C448(S3xC2xC4).9C4192,685
(S3×C2×C4).10C4 = C2×S3×M4(2)φ: C4/C2 → C2 ⊆ Out S3×C2×C448(S3xC2xC4).10C4192,1302
(S3×C2×C4).11C4 = D6⋊C16φ: C4/C2 → C2 ⊆ Out S3×C2×C496(S3xC2xC4).11C4192,66
(S3×C2×C4).12C4 = C42.282D6φ: C4/C2 → C2 ⊆ Out S3×C2×C496(S3xC2xC4).12C4192,244
(S3×C2×C4).13C4 = C4×C8⋊S3φ: C4/C2 → C2 ⊆ Out S3×C2×C496(S3xC2xC4).13C4192,246
(S3×C2×C4).14C4 = S3×C8⋊C4φ: C4/C2 → C2 ⊆ Out S3×C2×C496(S3xC2xC4).14C4192,263
(S3×C2×C4).15C4 = C42.182D6φ: C4/C2 → C2 ⊆ Out S3×C2×C496(S3xC2xC4).15C4192,264
(S3×C2×C4).16C4 = Dic3⋊5M4(2)φ: C4/C2 → C2 ⊆ Out S3×C2×C496(S3xC2xC4).16C4192,266
(S3×C2×C4).17C4 = S3×C22⋊C8φ: C4/C2 → C2 ⊆ Out S3×C2×C448(S3xC2xC4).17C4192,283
(S3×C2×C4).18C4 = D6⋊M4(2)φ: C4/C2 → C2 ⊆ Out S3×C2×C448(S3xC2xC4).18C4192,285
(S3×C2×C4).19C4 = C42.202D6φ: C4/C2 → C2 ⊆ Out S3×C2×C496(S3xC2xC4).19C4192,394
(S3×C2×C4).20C4 = C2×D6.C8φ: C4/C2 → C2 ⊆ Out S3×C2×C496(S3xC2xC4).20C4192,459
(S3×C2×C4).21C4 = C2×D6⋊C8φ: C4/C2 → C2 ⊆ Out S3×C2×C496(S3xC2xC4).21C4192,667
(S3×C2×C4).22C4 = C22×C8⋊S3φ: C4/C2 → C2 ⊆ Out S3×C2×C496(S3xC2xC4).22C4192,1296
(S3×C2×C4).23C4 = S3×C4×C8φ: trivial image96(S3xC2xC4).23C4192,243
(S3×C2×C4).24C4 = S3×C2×C16φ: trivial image96(S3xC2xC4).24C4192,458
(S3×C2×C4).25C4 = S3×C22×C8φ: trivial image96(S3xC2xC4).25C4192,1295

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