# Extensions 1→N→G→Q→1 with N=C2×C4○D4 and Q=S3

Direct product G=N×Q with N=C2×C4○D4 and Q=S3
dρLabelID
C2×S3×C4○D448C2xS3xC4oD4192,1520

Semidirect products G=N:Q with N=C2×C4○D4 and Q=S3
extensionφ:Q→Out NdρLabelID
(C2×C4○D4)⋊1S3 = SL2(𝔽3)⋊D4φ: S3/C1S3 ⊆ Out C2×C4○D432(C2xC4oD4):1S3192,986
(C2×C4○D4)⋊2S3 = C2×C4.6S4φ: S3/C1S3 ⊆ Out C2×C4○D432(C2xC4oD4):2S3192,1480
(C2×C4○D4)⋊3S3 = C2×C4.3S4φ: S3/C1S3 ⊆ Out C2×C4○D432(C2xC4oD4):3S3192,1481
(C2×C4○D4)⋊4S3 = GL2(𝔽3)⋊C22φ: S3/C1S3 ⊆ Out C2×C4○D4324(C2xC4oD4):4S3192,1482
(C2×C4○D4)⋊5S3 = (C3×D4)⋊14D4φ: S3/C3C2 ⊆ Out C2×C4○D496(C2xC4oD4):5S3192,797
(C2×C4○D4)⋊6S3 = C2×D4⋊D6φ: S3/C3C2 ⊆ Out C2×C4○D448(C2xC4oD4):6S3192,1379
(C2×C4○D4)⋊7S3 = C2×Q8.13D6φ: S3/C3C2 ⊆ Out C2×C4○D496(C2xC4oD4):7S3192,1380
(C2×C4○D4)⋊8S3 = C12.C24φ: S3/C3C2 ⊆ Out C2×C4○D4484(C2xC4oD4):8S3192,1381
(C2×C4○D4)⋊9S3 = C6.1042- 1+4φ: S3/C3C2 ⊆ Out C2×C4○D496(C2xC4oD4):9S3192,1383
(C2×C4○D4)⋊10S3 = (C2×D4)⋊43D6φ: S3/C3C2 ⊆ Out C2×C4○D448(C2xC4oD4):10S3192,1387
(C2×C4○D4)⋊11S3 = C6.1452+ 1+4φ: S3/C3C2 ⊆ Out C2×C4○D448(C2xC4oD4):11S3192,1388
(C2×C4○D4)⋊12S3 = C6.1462+ 1+4φ: S3/C3C2 ⊆ Out C2×C4○D448(C2xC4oD4):12S3192,1389
(C2×C4○D4)⋊13S3 = C6.1072- 1+4φ: S3/C3C2 ⊆ Out C2×C4○D496(C2xC4oD4):13S3192,1390
(C2×C4○D4)⋊14S3 = (C2×C12)⋊17D4φ: S3/C3C2 ⊆ Out C2×C4○D496(C2xC4oD4):14S3192,1391
(C2×C4○D4)⋊15S3 = C6.1082- 1+4φ: S3/C3C2 ⊆ Out C2×C4○D496(C2xC4oD4):15S3192,1392
(C2×C4○D4)⋊16S3 = C6.1482+ 1+4φ: S3/C3C2 ⊆ Out C2×C4○D496(C2xC4oD4):16S3192,1393
(C2×C4○D4)⋊17S3 = C2×D4○D12φ: S3/C3C2 ⊆ Out C2×C4○D448(C2xC4oD4):17S3192,1521
(C2×C4○D4)⋊18S3 = C2×Q8○D12φ: S3/C3C2 ⊆ Out C2×C4○D496(C2xC4oD4):18S3192,1522
(C2×C4○D4)⋊19S3 = C6.C25φ: S3/C3C2 ⊆ Out C2×C4○D4484(C2xC4oD4):19S3192,1523

Non-split extensions G=N.Q with N=C2×C4○D4 and Q=S3
extensionφ:Q→Out NdρLabelID
(C2×C4○D4).1S3 = C2×U2(𝔽3)φ: S3/C1S3 ⊆ Out C2×C4○D448(C2xC4oD4).1S3192,981
(C2×C4○D4).2S3 = U2(𝔽3)⋊C2φ: S3/C1S3 ⊆ Out C2×C4○D4324(C2xC4oD4).2S3192,982
(C2×C4○D4).3S3 = C4.A4⋊C4φ: S3/C1S3 ⊆ Out C2×C4○D464(C2xC4oD4).3S3192,983
(C2×C4○D4).4S3 = SL2(𝔽3).D4φ: S3/C1S3 ⊆ Out C2×C4○D464(C2xC4oD4).4S3192,984
(C2×C4○D4).5S3 = (C2×C4).S4φ: S3/C1S3 ⊆ Out C2×C4○D464(C2xC4oD4).5S3192,985
(C2×C4○D4).6S3 = C2×C4.S4φ: S3/C1S3 ⊆ Out C2×C4○D464(C2xC4oD4).6S3192,1479
(C2×C4○D4).7S3 = C4○D43Dic3φ: S3/C3C2 ⊆ Out C2×C4○D496(C2xC4oD4).7S3192,791
(C2×C4○D4).8S3 = C4○D44Dic3φ: S3/C3C2 ⊆ Out C2×C4○D496(C2xC4oD4).8S3192,792
(C2×C4○D4).9S3 = (C6×D4).11C4φ: S3/C3C2 ⊆ Out C2×C4○D496(C2xC4oD4).9S3192,793
(C2×C4○D4).10S3 = C2×Q83Dic3φ: S3/C3C2 ⊆ Out C2×C4○D448(C2xC4oD4).10S3192,794
(C2×C4○D4).11S3 = (C6×D4)⋊9C4φ: S3/C3C2 ⊆ Out C2×C4○D4484(C2xC4oD4).11S3192,795
(C2×C4○D4).12S3 = (C6×D4).16C4φ: S3/C3C2 ⊆ Out C2×C4○D4484(C2xC4oD4).12S3192,796
(C2×C4○D4).13S3 = (C3×D4).32D4φ: S3/C3C2 ⊆ Out C2×C4○D496(C2xC4oD4).13S3192,798
(C2×C4○D4).14S3 = (C6×D4)⋊10C4φ: S3/C3C2 ⊆ Out C2×C4○D4484(C2xC4oD4).14S3192,799
(C2×C4○D4).15S3 = C12.76C24φ: S3/C3C2 ⊆ Out C2×C4○D4484(C2xC4oD4).15S3192,1378
(C2×C4○D4).16S3 = C2×Q8.14D6φ: S3/C3C2 ⊆ Out C2×C4○D496(C2xC4oD4).16S3192,1382
(C2×C4○D4).17S3 = C6.1052- 1+4φ: S3/C3C2 ⊆ Out C2×C4○D496(C2xC4oD4).17S3192,1384
(C2×C4○D4).18S3 = C6.1442+ 1+4φ: S3/C3C2 ⊆ Out C2×C4○D496(C2xC4oD4).18S3192,1386
(C2×C4○D4).19S3 = C2×D4.Dic3φ: trivial image96(C2xC4oD4).19S3192,1377
(C2×C4○D4).20S3 = Dic3×C4○D4φ: trivial image96(C2xC4oD4).20S3192,1385

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