# Extensions 1→N→G→Q→1 with N=C23×C4 and Q=S3

Direct product G=N×Q with N=C23×C4 and Q=S3
dρLabelID
S3×C23×C496S3xC2^3xC4192,1511

Semidirect products G=N:Q with N=C23×C4 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C23×C4)⋊1S3 = C24.5D6φ: S3/C1S3 ⊆ Aut C23×C424(C2^3xC4):1S3192,972
(C23×C4)⋊2S3 = C2×C4×S4φ: S3/C1S3 ⊆ Aut C23×C424(C2^3xC4):2S3192,1469
(C23×C4)⋊3S3 = C2×C4⋊S4φ: S3/C1S3 ⊆ Aut C23×C424(C2^3xC4):3S3192,1470
(C23×C4)⋊4S3 = C24.10D6φ: S3/C1S3 ⊆ Aut C23×C4246(C2^3xC4):4S3192,1471
(C23×C4)⋊5S3 = C24.76D6φ: S3/C3C2 ⊆ Aut C23×C496(C2^3xC4):5S3192,772
(C23×C4)⋊6S3 = C22×D6⋊C4φ: S3/C3C2 ⊆ Aut C23×C496(C2^3xC4):6S3192,1346
(C23×C4)⋊7S3 = C2×C4×C3⋊D4φ: S3/C3C2 ⊆ Aut C23×C496(C2^3xC4):7S3192,1347
(C23×C4)⋊8S3 = C2×C23.28D6φ: S3/C3C2 ⊆ Aut C23×C496(C2^3xC4):8S3192,1348
(C23×C4)⋊9S3 = C2×C127D4φ: S3/C3C2 ⊆ Aut C23×C496(C2^3xC4):9S3192,1349
(C23×C4)⋊10S3 = C24.83D6φ: S3/C3C2 ⊆ Aut C23×C448(C2^3xC4):10S3192,1350
(C23×C4)⋊11S3 = C23×D12φ: S3/C3C2 ⊆ Aut C23×C496(C2^3xC4):11S3192,1512
(C23×C4)⋊12S3 = C22×C4○D12φ: S3/C3C2 ⊆ Aut C23×C496(C2^3xC4):12S3192,1513

Non-split extensions G=N.Q with N=C23×C4 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C23×C4).1S3 = C2×A4⋊C8φ: S3/C1S3 ⊆ Aut C23×C448(C2^3xC4).1S3192,967
(C23×C4).2S3 = C4×A4⋊C4φ: S3/C1S3 ⊆ Aut C23×C448(C2^3xC4).2S3192,969
(C23×C4).3S3 = C24.3D6φ: S3/C1S3 ⊆ Aut C23×C448(C2^3xC4).3S3192,970
(C23×C4).4S3 = A4⋊M4(2)φ: S3/C1S3 ⊆ Aut C23×C4246(C2^3xC4).4S3192,968
(C23×C4).5S3 = C24.4D6φ: S3/C1S3 ⊆ Aut C23×C448(C2^3xC4).5S3192,971
(C23×C4).6S3 = C2×A4⋊Q8φ: S3/C1S3 ⊆ Aut C23×C448(C2^3xC4).6S3192,1468
(C23×C4).7S3 = C2×C12.55D4φ: S3/C3C2 ⊆ Aut C23×C496(C2^3xC4).7S3192,765
(C23×C4).8S3 = C2×C6.C42φ: S3/C3C2 ⊆ Aut C23×C4192(C2^3xC4).8S3192,767
(C23×C4).9S3 = C4×C6.D4φ: S3/C3C2 ⊆ Aut C23×C496(C2^3xC4).9S3192,768
(C23×C4).10S3 = C24.73D6φ: S3/C3C2 ⊆ Aut C23×C496(C2^3xC4).10S3192,769
(C23×C4).11S3 = C24.74D6φ: S3/C3C2 ⊆ Aut C23×C496(C2^3xC4).11S3192,770
(C23×C4).12S3 = C22×Dic3⋊C4φ: S3/C3C2 ⊆ Aut C23×C4192(C2^3xC4).12S3192,1342
(C23×C4).13S3 = C24.6Dic3φ: S3/C3C2 ⊆ Aut C23×C448(C2^3xC4).13S3192,766
(C23×C4).14S3 = C24.75D6φ: S3/C3C2 ⊆ Aut C23×C496(C2^3xC4).14S3192,771
(C23×C4).15S3 = C22×C4.Dic3φ: S3/C3C2 ⊆ Aut C23×C496(C2^3xC4).15S3192,1340
(C23×C4).16S3 = C2×C12.48D4φ: S3/C3C2 ⊆ Aut C23×C496(C2^3xC4).16S3192,1343
(C23×C4).17S3 = C22×C4⋊Dic3φ: S3/C3C2 ⊆ Aut C23×C4192(C2^3xC4).17S3192,1344
(C23×C4).18S3 = C2×C23.26D6φ: S3/C3C2 ⊆ Aut C23×C496(C2^3xC4).18S3192,1345
(C23×C4).19S3 = C23×Dic6φ: S3/C3C2 ⊆ Aut C23×C4192(C2^3xC4).19S3192,1510
(C23×C4).20S3 = C23×C3⋊C8central extension (φ=1)192(C2^3xC4).20S3192,1339
(C23×C4).21S3 = Dic3×C22×C4central extension (φ=1)192(C2^3xC4).21S3192,1341

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