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Extensions 1→N→G→Q→1 with N=C3×C12 and Q=Q8

Direct product G=N×Q with N=C3×C12 and Q=Q8
dρLabelID
Q8×C3×C12288Q8xC3xC12288,816

Semidirect products G=N:Q with N=C3×C12 and Q=Q8
extensionφ:Q→Aut NdρLabelID
(C3×C12)⋊1Q8 = C4×PSU3(𝔽2)φ: Q8/C1 → Q8 ⊆ Aut C3×C12368(C3xC12):1Q8288,892
(C3×C12)⋊2Q8 = C4⋊PSU3(𝔽2)φ: Q8/C1 → Q8 ⊆ Aut C3×C12368(C3xC12):2Q8288,893
(C3×C12)⋊3Q8 = C12⋊3Dic6φ: Q8/C2 → C22 ⊆ Aut C3×C1296(C3xC12):3Q8288,566
(C3×C12)⋊4Q8 = C12⋊Dic6φ: Q8/C2 → C22 ⊆ Aut C3×C1296(C3xC12):4Q8288,567
(C3×C12)⋊5Q8 = C3×C12⋊Q8φ: Q8/C2 → C22 ⊆ Aut C3×C1296(C3xC12):5Q8288,659
(C3×C12)⋊6Q8 = C12⋊2Dic6φ: Q8/C2 → C22 ⊆ Aut C3×C12288(C3xC12):6Q8288,745
(C3×C12)⋊7Q8 = C4×C32⋊2Q8φ: Q8/C2 → C22 ⊆ Aut C3×C1296(C3xC12):7Q8288,565
(C3×C12)⋊8Q8 = C12⋊6Dic6φ: Q8/C4 → C2 ⊆ Aut C3×C12288(C3xC12):8Q8288,726
(C3×C12)⋊9Q8 = C3×C12⋊2Q8φ: Q8/C4 → C2 ⊆ Aut C3×C1296(C3xC12):9Q8288,640
(C3×C12)⋊10Q8 = C12×Dic6φ: Q8/C4 → C2 ⊆ Aut C3×C1296(C3xC12):10Q8288,639
(C3×C12)⋊11Q8 = C4×C32⋊4Q8φ: Q8/C4 → C2 ⊆ Aut C3×C12288(C3xC12):11Q8288,725
(C3×C12)⋊12Q8 = C32×C4⋊Q8φ: Q8/C4 → C2 ⊆ Aut C3×C12288(C3xC12):12Q8288,825

Non-split extensions G=N.Q with N=C3×C12 and Q=Q8
extensionφ:Q→Aut NdρLabelID
(C3×C12).1Q8 = C4.4PSU3(𝔽2)φ: Q8/C1 → Q8 ⊆ Aut C3×C12488(C3xC12).1Q8288,392
(C3×C12).2Q8 = C4.PSU3(𝔽2)φ: Q8/C1 → Q8 ⊆ Aut C3×C12488(C3xC12).2Q8288,393
(C3×C12).3Q8 = C4.2PSU3(𝔽2)φ: Q8/C1 → Q8 ⊆ Aut C3×C12488(C3xC12).3Q8288,394
(C3×C12).4Q8 = C4.3PSU3(𝔽2)φ: Q8/C1 → Q8 ⊆ Aut C3×C12488(C3xC12).4Q8288,891
(C3×C12).5Q8 = C12.Dic6φ: Q8/C2 → C22 ⊆ Aut C3×C1296(C3xC12).5Q8288,221
(C3×C12).6Q8 = C12.6Dic6φ: Q8/C2 → C22 ⊆ Aut C3×C1296(C3xC12).6Q8288,222
(C3×C12).7Q8 = C6.18D24φ: Q8/C2 → C22 ⊆ Aut C3×C1296(C3xC12).7Q8288,223
(C3×C12).8Q8 = C12.8Dic6φ: Q8/C2 → C22 ⊆ Aut C3×C1296(C3xC12).8Q8288,224
(C3×C12).9Q8 = C3×C6.Q16φ: Q8/C2 → C22 ⊆ Aut C3×C1296(C3xC12).9Q8288,241
(C3×C12).10Q8 = C3×C12.Q8φ: Q8/C2 → C22 ⊆ Aut C3×C1296(C3xC12).10Q8288,242
(C3×C12).11Q8 = C12.9Dic6φ: Q8/C2 → C22 ⊆ Aut C3×C12288(C3xC12).11Q8288,282
(C3×C12).12Q8 = C12.10Dic6φ: Q8/C2 → C22 ⊆ Aut C3×C12288(C3xC12).12Q8288,283
(C3×C12).13Q8 = C62.39C23φ: Q8/C2 → C22 ⊆ Aut C3×C1296(C3xC12).13Q8288,517
(C3×C12).14Q8 = C62.42C23φ: Q8/C2 → C22 ⊆ Aut C3×C1296(C3xC12).14Q8288,520
(C3×C12).15Q8 = C3×C4.Dic6φ: Q8/C2 → C22 ⊆ Aut C3×C1296(C3xC12).15Q8288,661
(C3×C12).16Q8 = C62.234C23φ: Q8/C2 → C22 ⊆ Aut C3×C12288(C3xC12).16Q8288,747
(C3×C12).17Q8 = C12.81D12φ: Q8/C2 → C22 ⊆ Aut C3×C1296(C3xC12).17Q8288,219
(C3×C12).18Q8 = C12.15Dic6φ: Q8/C2 → C22 ⊆ Aut C3×C1296(C3xC12).18Q8288,220
(C3×C12).19Q8 = C24⋊2Dic3φ: Q8/C4 → C2 ⊆ Aut C3×C12288(C3xC12).19Q8288,292
(C3×C12).20Q8 = C24⋊1Dic3φ: Q8/C4 → C2 ⊆ Aut C3×C12288(C3xC12).20Q8288,293
(C3×C12).21Q8 = C12.25Dic6φ: Q8/C4 → C2 ⊆ Aut C3×C12288(C3xC12).21Q8288,727
(C3×C12).22Q8 = C3×C8⋊Dic3φ: Q8/C4 → C2 ⊆ Aut C3×C1296(C3xC12).22Q8288,251
(C3×C12).23Q8 = C3×C24⋊1C4φ: Q8/C4 → C2 ⊆ Aut C3×C1296(C3xC12).23Q8288,252
(C3×C12).24Q8 = C3×C12.6Q8φ: Q8/C4 → C2 ⊆ Aut C3×C1296(C3xC12).24Q8288,641
(C3×C12).25Q8 = C3×C12⋊C8φ: Q8/C4 → C2 ⊆ Aut C3×C1296(C3xC12).25Q8288,238
(C3×C12).26Q8 = C3×Dic3⋊C8φ: Q8/C4 → C2 ⊆ Aut C3×C1296(C3xC12).26Q8288,248
(C3×C12).27Q8 = C12.57D12φ: Q8/C4 → C2 ⊆ Aut C3×C12288(C3xC12).27Q8288,279
(C3×C12).28Q8 = C12.30Dic6φ: Q8/C4 → C2 ⊆ Aut C3×C12288(C3xC12).28Q8288,289
(C3×C12).29Q8 = C32×C4.Q8φ: Q8/C4 → C2 ⊆ Aut C3×C12288(C3xC12).29Q8288,324
(C3×C12).30Q8 = C32×C2.D8φ: Q8/C4 → C2 ⊆ Aut C3×C12288(C3xC12).30Q8288,325
(C3×C12).31Q8 = C32×C42.C2φ: Q8/C4 → C2 ⊆ Aut C3×C12288(C3xC12).31Q8288,822
(C3×C12).32Q8 = C32×C4⋊C8central extension (φ=1)288(C3xC12).32Q8288,323

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