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Extensions 1→N→G→Q→1 with N=C2×C24 and Q=S3

Direct product G=N×Q with N=C2×C24 and Q=S3
dρLabelID
S3×C2×C2496S3xC2xC24288,670

Semidirect products G=N:Q with N=C2×C24 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C2×C24)⋊1S3 = C3×D6⋊C8φ: S3/C3 → C2 ⊆ Aut C2×C2496(C2xC24):1S3288,254
(C2×C24)⋊2S3 = C3×C2.D24φ: S3/C3 → C2 ⊆ Aut C2×C2496(C2xC24):2S3288,255
(C2×C24)⋊3S3 = C12.60D12φ: S3/C3 → C2 ⊆ Aut C2×C24144(C2xC24):3S3288,295
(C2×C24)⋊4S3 = C62.84D4φ: S3/C3 → C2 ⊆ Aut C2×C24144(C2xC24):4S3288,296
(C2×C24)⋊5S3 = C2×C32⋊5D8φ: S3/C3 → C2 ⊆ Aut C2×C24144(C2xC24):5S3288,760
(C2×C24)⋊6S3 = C24.78D6φ: S3/C3 → C2 ⊆ Aut C2×C24144(C2xC24):6S3288,761
(C2×C24)⋊7S3 = C2×C24⋊2S3φ: S3/C3 → C2 ⊆ Aut C2×C24144(C2xC24):7S3288,759
(C2×C24)⋊8S3 = C6×D24φ: S3/C3 → C2 ⊆ Aut C2×C2496(C2xC24):8S3288,674
(C2×C24)⋊9S3 = C3×C4○D24φ: S3/C3 → C2 ⊆ Aut C2×C24482(C2xC24):9S3288,675
(C2×C24)⋊10S3 = C2×C8×C3⋊S3φ: S3/C3 → C2 ⊆ Aut C2×C24144(C2xC24):10S3288,756
(C2×C24)⋊11S3 = C2×C24⋊S3φ: S3/C3 → C2 ⊆ Aut C2×C24144(C2xC24):11S3288,757
(C2×C24)⋊12S3 = C24.95D6φ: S3/C3 → C2 ⊆ Aut C2×C24144(C2xC24):12S3288,758
(C2×C24)⋊13S3 = C6×C24⋊C2φ: S3/C3 → C2 ⊆ Aut C2×C2496(C2xC24):13S3288,673
(C2×C24)⋊14S3 = C6×C8⋊S3φ: S3/C3 → C2 ⊆ Aut C2×C2496(C2xC24):14S3288,671
(C2×C24)⋊15S3 = C3×C8○D12φ: S3/C3 → C2 ⊆ Aut C2×C24482(C2xC24):15S3288,672

Non-split extensions G=N.Q with N=C2×C24 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C2×C24).1S3 = Dic9⋊C8φ: S3/C3 → C2 ⊆ Aut C2×C24288(C2xC24).1S3288,22
(C2×C24).2S3 = C36.45D4φ: S3/C3 → C2 ⊆ Aut C2×C24288(C2xC24).2S3288,24
(C2×C24).3S3 = D18⋊C8φ: S3/C3 → C2 ⊆ Aut C2×C24144(C2xC24).3S3288,27
(C2×C24).4S3 = C2.D72φ: S3/C3 → C2 ⊆ Aut C2×C24144(C2xC24).4S3288,28
(C2×C24).5S3 = C3×Dic3⋊C8φ: S3/C3 → C2 ⊆ Aut C2×C2496(C2xC24).5S3288,248
(C2×C24).6S3 = C3×C2.Dic12φ: S3/C3 → C2 ⊆ Aut C2×C2496(C2xC24).6S3288,250
(C2×C24).7S3 = C12.30Dic6φ: S3/C3 → C2 ⊆ Aut C2×C24288(C2xC24).7S3288,289
(C2×C24).8S3 = C6.4Dic12φ: S3/C3 → C2 ⊆ Aut C2×C24288(C2xC24).8S3288,291
(C2×C24).9S3 = C72⋊1C4φ: S3/C3 → C2 ⊆ Aut C2×C24288(C2xC24).9S3288,26
(C2×C24).10S3 = C2×Dic36φ: S3/C3 → C2 ⊆ Aut C2×C24288(C2xC24).10S3288,109
(C2×C24).11S3 = C2×D72φ: S3/C3 → C2 ⊆ Aut C2×C24144(C2xC24).11S3288,114
(C2×C24).12S3 = C24⋊1Dic3φ: S3/C3 → C2 ⊆ Aut C2×C24288(C2xC24).12S3288,293
(C2×C24).13S3 = C2×C32⋊5Q16φ: S3/C3 → C2 ⊆ Aut C2×C24288(C2xC24).13S3288,762
(C2×C24).14S3 = C72.C4φ: S3/C3 → C2 ⊆ Aut C2×C241442(C2xC24).14S3288,20
(C2×C24).15S3 = D72⋊7C2φ: S3/C3 → C2 ⊆ Aut C2×C241442(C2xC24).15S3288,115
(C2×C24).16S3 = C12.59D12φ: S3/C3 → C2 ⊆ Aut C2×C24144(C2xC24).16S3288,294
(C2×C24).17S3 = C8⋊Dic9φ: S3/C3 → C2 ⊆ Aut C2×C24288(C2xC24).17S3288,25
(C2×C24).18S3 = C2×C72⋊C2φ: S3/C3 → C2 ⊆ Aut C2×C24144(C2xC24).18S3288,113
(C2×C24).19S3 = C24⋊2Dic3φ: S3/C3 → C2 ⊆ Aut C2×C24288(C2xC24).19S3288,292
(C2×C24).20S3 = C3×C24⋊1C4φ: S3/C3 → C2 ⊆ Aut C2×C2496(C2xC24).20S3288,252
(C2×C24).21S3 = C6×Dic12φ: S3/C3 → C2 ⊆ Aut C2×C2496(C2xC24).21S3288,676
(C2×C24).22S3 = C3×C24.C4φ: S3/C3 → C2 ⊆ Aut C2×C24482(C2xC24).22S3288,253
(C2×C24).23S3 = C2×C9⋊C16φ: S3/C3 → C2 ⊆ Aut C2×C24288(C2xC24).23S3288,18
(C2×C24).24S3 = C36.C8φ: S3/C3 → C2 ⊆ Aut C2×C241442(C2xC24).24S3288,19
(C2×C24).25S3 = C8×Dic9φ: S3/C3 → C2 ⊆ Aut C2×C24288(C2xC24).25S3288,21
(C2×C24).26S3 = C72⋊C4φ: S3/C3 → C2 ⊆ Aut C2×C24288(C2xC24).26S3288,23
(C2×C24).27S3 = C2×C8×D9φ: S3/C3 → C2 ⊆ Aut C2×C24144(C2xC24).27S3288,110
(C2×C24).28S3 = C2×C8⋊D9φ: S3/C3 → C2 ⊆ Aut C2×C24144(C2xC24).28S3288,111
(C2×C24).29S3 = D36.2C4φ: S3/C3 → C2 ⊆ Aut C2×C241442(C2xC24).29S3288,112
(C2×C24).30S3 = C2×C24.S3φ: S3/C3 → C2 ⊆ Aut C2×C24288(C2xC24).30S3288,286
(C2×C24).31S3 = C24.94D6φ: S3/C3 → C2 ⊆ Aut C2×C24144(C2xC24).31S3288,287
(C2×C24).32S3 = C8×C3⋊Dic3φ: S3/C3 → C2 ⊆ Aut C2×C24288(C2xC24).32S3288,288
(C2×C24).33S3 = C24⋊Dic3φ: S3/C3 → C2 ⊆ Aut C2×C24288(C2xC24).33S3288,290
(C2×C24).34S3 = C3×C8⋊Dic3φ: S3/C3 → C2 ⊆ Aut C2×C2496(C2xC24).34S3288,251
(C2×C24).35S3 = C3×C12.C8φ: S3/C3 → C2 ⊆ Aut C2×C24482(C2xC24).35S3288,246
(C2×C24).36S3 = C3×C24⋊C4φ: S3/C3 → C2 ⊆ Aut C2×C2496(C2xC24).36S3288,249
(C2×C24).37S3 = C6×C3⋊C16central extension (φ=1)96(C2xC24).37S3288,245
(C2×C24).38S3 = Dic3×C24central extension (φ=1)96(C2xC24).38S3288,247

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