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Extensions 1→N→G→Q→1 with N=C6×C4⋊C4 and Q=C2

Direct product G=N×Q with N=C6×C4⋊C4 and Q=C2
dρLabelID
C2×C6×C4⋊C4192C2xC6xC4:C4192,1402

Semidirect products G=N:Q with N=C6×C4⋊C4 and Q=C2
extensionφ:Q→Out NdρLabelID
(C6×C4⋊C4)⋊1C2 = C2×C6.D8φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):1C2192,524
(C6×C4⋊C4)⋊2C2 = C4○D12⋊C4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):2C2192,525
(C6×C4⋊C4)⋊3C2 = (C2×C6).40D8φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):3C2192,526
(C6×C4⋊C4)⋊4C2 = C4⋊C4.228D6φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):4C2192,527
(C6×C4⋊C4)⋊5C2 = C4⋊(D6⋊C4)φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):5C2192,546
(C6×C4⋊C4)⋊6C2 = (C2×D12)⋊10C4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):6C2192,547
(C6×C4⋊C4)⋊7C2 = C2×S3×C4⋊C4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):7C2192,1060
(C6×C4⋊C4)⋊8C2 = C2×C4⋊C4⋊7S3φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):8C2192,1061
(C6×C4⋊C4)⋊9C2 = C2×Dic3⋊5D4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):9C2192,1062
(C6×C4⋊C4)⋊10C2 = C6.82+ 1+4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):10C2192,1063
(C6×C4⋊C4)⋊11C2 = C2×D6.D4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):11C2192,1064
(C6×C4⋊C4)⋊12C2 = C2×C12⋊D4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):12C2192,1065
(C6×C4⋊C4)⋊13C2 = C6.2- 1+4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):13C2192,1066
(C6×C4⋊C4)⋊14C2 = C2×D6⋊Q8φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):14C2192,1067
(C6×C4⋊C4)⋊15C2 = C2×C4.D12φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):15C2192,1068
(C6×C4⋊C4)⋊16C2 = C6.2+ 1+4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):16C2192,1069
(C6×C4⋊C4)⋊17C2 = C6.102+ 1+4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):17C2192,1070
(C6×C4⋊C4)⋊18C2 = C2×C4⋊C4⋊S3φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):18C2192,1071
(C6×C4⋊C4)⋊19C2 = C6.52- 1+4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):19C2192,1072
(C6×C4⋊C4)⋊20C2 = C6.112+ 1+4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):20C2192,1073
(C6×C4⋊C4)⋊21C2 = C6.62- 1+4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):21C2192,1074
(C6×C4⋊C4)⋊22C2 = (C2×C4)⋊3D12φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):22C2192,550
(C6×C4⋊C4)⋊23C2 = (C2×C12).56D4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):23C2192,553
(C6×C4⋊C4)⋊24C2 = D6⋊C4⋊6C4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):24C2192,548
(C6×C4⋊C4)⋊25C2 = D6⋊C4⋊7C4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):25C2192,549
(C6×C4⋊C4)⋊26C2 = (C2×C12).289D4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):26C2192,551
(C6×C4⋊C4)⋊27C2 = (C2×C12).290D4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):27C2192,552
(C6×C4⋊C4)⋊28C2 = C3×C23.7Q8φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):28C2192,813
(C6×C4⋊C4)⋊29C2 = C3×C23.8Q8φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):29C2192,818
(C6×C4⋊C4)⋊30C2 = C3×C24.C22φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):30C2192,821
(C6×C4⋊C4)⋊31C2 = C3×C24.3C22φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):31C2192,823
(C6×C4⋊C4)⋊32C2 = C3×C23.10D4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):32C2192,827
(C6×C4⋊C4)⋊33C2 = C3×C23.Q8φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):33C2192,829
(C6×C4⋊C4)⋊34C2 = C3×C23.11D4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):34C2192,830
(C6×C4⋊C4)⋊35C2 = C3×C23.4Q8φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):35C2192,832
(C6×C4⋊C4)⋊36C2 = C6×D4⋊C4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):36C2192,847
(C6×C4⋊C4)⋊37C2 = C3×C23.36D4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):37C2192,850
(C6×C4⋊C4)⋊38C2 = C3×C22.D8φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):38C2192,913
(C6×C4⋊C4)⋊39C2 = C3×C23.46D4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):39C2192,914
(C6×C4⋊C4)⋊40C2 = C3×C23.33C23φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):40C2192,1409
(C6×C4⋊C4)⋊41C2 = C6×C4⋊D4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):41C2192,1411
(C6×C4⋊C4)⋊42C2 = C6×C22⋊Q8φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):42C2192,1412
(C6×C4⋊C4)⋊43C2 = C6×C22.D4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):43C2192,1413
(C6×C4⋊C4)⋊44C2 = C6×C42⋊2C2φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):44C2192,1417
(C6×C4⋊C4)⋊45C2 = C3×C22.31C24φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):45C2192,1426
(C6×C4⋊C4)⋊46C2 = C3×C22.33C24φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):46C2192,1428
(C6×C4⋊C4)⋊47C2 = C3×D4⋊6D4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):47C2192,1436
(C6×C4⋊C4)⋊48C2 = C3×C22.46C24φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):48C2192,1441
(C6×C4⋊C4)⋊49C2 = C3×C22.47C24φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):49C2192,1442
(C6×C4⋊C4)⋊50C2 = C3×D4⋊3Q8φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4):50C2192,1443
(C6×C4⋊C4)⋊51C2 = C6×C42⋊C2φ: trivial image96(C6xC4:C4):51C2192,1403
(C6×C4⋊C4)⋊52C2 = D4×C2×C12φ: trivial image96(C6xC4:C4):52C2192,1404

Non-split extensions G=N.Q with N=C6×C4⋊C4 and Q=C2
extensionφ:Q→Out NdρLabelID
(C6×C4⋊C4).1C2 = C12.C42φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).1C2192,88
(C6×C4⋊C4).2C2 = C12.(C4⋊C4)φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4).2C2192,89
(C6×C4⋊C4).3C2 = C2×C6.Q16φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).3C2192,521
(C6×C4⋊C4).4C2 = C2×C12.Q8φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).4C2192,522
(C6×C4⋊C4).5C2 = C4⋊C4.225D6φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4).5C2192,523
(C6×C4⋊C4).6C2 = C2×C6.SD16φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).6C2192,528
(C6×C4⋊C4).7C2 = C4⋊C4.230D6φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4).7C2192,529
(C6×C4⋊C4).8C2 = C4⋊C4.231D6φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4).8C2192,530
(C6×C4⋊C4).9C2 = C12⋊(C4⋊C4)φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).9C2192,531
(C6×C4⋊C4).10C2 = C4.(D6⋊C4)φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).10C2192,532
(C6×C4⋊C4).11C2 = Dic3×C4⋊C4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).11C2192,533
(C6×C4⋊C4).12C2 = (C4×Dic3)⋊8C4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).12C2192,534
(C6×C4⋊C4).13C2 = (C4×Dic3)⋊9C4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).13C2192,536
(C6×C4⋊C4).14C2 = C4⋊C4⋊5Dic3φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).14C2192,539
(C6×C4⋊C4).15C2 = C4⋊C4⋊6Dic3φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).15C2192,543
(C6×C4⋊C4).16C2 = C2×Dic6⋊C4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).16C2192,1055
(C6×C4⋊C4).17C2 = C2×C12⋊Q8φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).17C2192,1056
(C6×C4⋊C4).18C2 = C2×Dic3.Q8φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).18C2192,1057
(C6×C4⋊C4).19C2 = C2×C4.Dic6φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).19C2192,1058
(C6×C4⋊C4).20C2 = C6.72+ 1+4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4).20C2192,1059
(C6×C4⋊C4).21C2 = (C2×Dic3)⋊Q8φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).21C2192,538
(C6×C4⋊C4).22C2 = (C2×C4).44D12φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).22C2192,540
(C6×C4⋊C4).23C2 = (C2×C12).54D4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).23C2192,541
(C6×C4⋊C4).24C2 = (C2×C12).55D4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).24C2192,545
(C6×C4⋊C4).25C2 = (C2×C12)⋊C8φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4).25C2192,87
(C6×C4⋊C4).26C2 = Dic3⋊(C4⋊C4)φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).26C2192,535
(C6×C4⋊C4).27C2 = C6.67(C4×D4)φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).27C2192,537
(C6×C4⋊C4).28C2 = C3×C22.M4(2)φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4).28C2192,130
(C6×C4⋊C4).29C2 = C3×C22.4Q16φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).29C2192,146
(C6×C4⋊C4).30C2 = C3×C22.C42φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4).30C2192,149
(C6×C4⋊C4).31C2 = (C2×Dic3).Q8φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).31C2192,542
(C6×C4⋊C4).32C2 = (C2×C12).288D4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).32C2192,544
(C6×C4⋊C4).33C2 = C3×C42⋊8C4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).33C2192,815
(C6×C4⋊C4).34C2 = C3×C42⋊9C4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).34C2192,817
(C6×C4⋊C4).35C2 = C3×C23.63C23φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).35C2192,820
(C6×C4⋊C4).36C2 = C3×C23.65C23φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).36C2192,822
(C6×C4⋊C4).37C2 = C3×C23.67C23φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).37C2192,824
(C6×C4⋊C4).38C2 = C3×C23.78C23φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).38C2192,828
(C6×C4⋊C4).39C2 = C3×C23.81C23φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).39C2192,831
(C6×C4⋊C4).40C2 = C3×C23.83C23φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).40C2192,833
(C6×C4⋊C4).41C2 = C6×Q8⋊C4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).41C2192,848
(C6×C4⋊C4).42C2 = C6×C4.Q8φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).42C2192,858
(C6×C4⋊C4).43C2 = C6×C2.D8φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).43C2192,859
(C6×C4⋊C4).44C2 = C3×M4(2)⋊C4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4).44C2192,861
(C6×C4⋊C4).45C2 = C3×C23.47D4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4).45C2192,916
(C6×C4⋊C4).46C2 = C3×C23.48D4φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4).46C2192,917
(C6×C4⋊C4).47C2 = C6×C42.C2φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).47C2192,1416
(C6×C4⋊C4).48C2 = C6×C4⋊Q8φ: C2/C1 → C2 ⊆ Out C6×C4⋊C4192(C6xC4:C4).48C2192,1420
(C6×C4⋊C4).49C2 = C3×C23.41C23φ: C2/C1 → C2 ⊆ Out C6×C4⋊C496(C6xC4:C4).49C2192,1433
(C6×C4⋊C4).50C2 = C12×C4⋊C4φ: trivial image192(C6xC4:C4).50C2192,811
(C6×C4⋊C4).51C2 = Q8×C2×C12φ: trivial image192(C6xC4:C4).51C2192,1405

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