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

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

Semidirect products G=N:Q with N=C2×C4⋊C4 and Q=C6
extensionφ:Q→Out NdρLabelID
(C2×C4⋊C4)⋊1C6 = C3×C23.7Q8φ: C6/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):1C6192,813
(C2×C4⋊C4)⋊2C6 = C3×C23.8Q8φ: C6/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):2C6192,818
(C2×C4⋊C4)⋊3C6 = C3×C24.C22φ: C6/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):3C6192,821
(C2×C4⋊C4)⋊4C6 = C3×C24.3C22φ: C6/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):4C6192,823
(C2×C4⋊C4)⋊5C6 = C3×C23.10D4φ: C6/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):5C6192,827
(C2×C4⋊C4)⋊6C6 = C3×C23.Q8φ: C6/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):6C6192,829
(C2×C4⋊C4)⋊7C6 = C3×C23.11D4φ: C6/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):7C6192,830
(C2×C4⋊C4)⋊8C6 = C3×C23.4Q8φ: C6/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):8C6192,832
(C2×C4⋊C4)⋊9C6 = C6×D4⋊C4φ: C6/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):9C6192,847
(C2×C4⋊C4)⋊10C6 = C3×C23.36D4φ: C6/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):10C6192,850
(C2×C4⋊C4)⋊11C6 = C3×C22.D8φ: C6/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):11C6192,913
(C2×C4⋊C4)⋊12C6 = C3×C23.46D4φ: C6/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):12C6192,914
(C2×C4⋊C4)⋊13C6 = C3×C23.33C23φ: C6/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):13C6192,1409
(C2×C4⋊C4)⋊14C6 = C6×C4⋊D4φ: C6/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):14C6192,1411
(C2×C4⋊C4)⋊15C6 = C6×C22⋊Q8φ: C6/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):15C6192,1412
(C2×C4⋊C4)⋊16C6 = C6×C22.D4φ: C6/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):16C6192,1413
(C2×C4⋊C4)⋊17C6 = C6×C42⋊2C2φ: C6/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):17C6192,1417
(C2×C4⋊C4)⋊18C6 = C3×C22.31C24φ: C6/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):18C6192,1426
(C2×C4⋊C4)⋊19C6 = C3×C22.33C24φ: C6/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):19C6192,1428
(C2×C4⋊C4)⋊20C6 = C3×D4⋊6D4φ: C6/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):20C6192,1436
(C2×C4⋊C4)⋊21C6 = C3×C22.46C24φ: C6/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):21C6192,1441
(C2×C4⋊C4)⋊22C6 = C3×C22.47C24φ: C6/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):22C6192,1442
(C2×C4⋊C4)⋊23C6 = C3×D4⋊3Q8φ: C6/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4):23C6192,1443
(C2×C4⋊C4)⋊24C6 = C6×C42⋊C2φ: trivial image96(C2xC4:C4):24C6192,1403
(C2×C4⋊C4)⋊25C6 = D4×C2×C12φ: trivial image96(C2xC4:C4):25C6192,1404

Non-split extensions G=N.Q with N=C2×C4⋊C4 and Q=C6
extensionφ:Q→Out NdρLabelID
(C2×C4⋊C4).1C6 = C3×C22.M4(2)φ: C6/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4).1C6192,130
(C2×C4⋊C4).2C6 = C3×C22.4Q16φ: C6/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).2C6192,146
(C2×C4⋊C4).3C6 = C3×C22.C42φ: C6/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4).3C6192,149
(C2×C4⋊C4).4C6 = C3×C42⋊8C4φ: C6/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).4C6192,815
(C2×C4⋊C4).5C6 = C3×C42⋊9C4φ: C6/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).5C6192,817
(C2×C4⋊C4).6C6 = C3×C23.63C23φ: C6/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).6C6192,820
(C2×C4⋊C4).7C6 = C3×C23.65C23φ: C6/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).7C6192,822
(C2×C4⋊C4).8C6 = C3×C23.67C23φ: C6/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).8C6192,824
(C2×C4⋊C4).9C6 = C3×C23.78C23φ: C6/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).9C6192,828
(C2×C4⋊C4).10C6 = C3×C23.81C23φ: C6/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).10C6192,831
(C2×C4⋊C4).11C6 = C3×C23.83C23φ: C6/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).11C6192,833
(C2×C4⋊C4).12C6 = C6×Q8⋊C4φ: C6/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).12C6192,848
(C2×C4⋊C4).13C6 = C6×C4.Q8φ: C6/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).13C6192,858
(C2×C4⋊C4).14C6 = C6×C2.D8φ: C6/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).14C6192,859
(C2×C4⋊C4).15C6 = C3×M4(2)⋊C4φ: C6/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4).15C6192,861
(C2×C4⋊C4).16C6 = C3×C23.47D4φ: C6/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4).16C6192,916
(C2×C4⋊C4).17C6 = C3×C23.48D4φ: C6/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4).17C6192,917
(C2×C4⋊C4).18C6 = C6×C42.C2φ: C6/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).18C6192,1416
(C2×C4⋊C4).19C6 = C6×C4⋊Q8φ: C6/C3 → C2 ⊆ Out C2×C4⋊C4192(C2xC4:C4).19C6192,1420
(C2×C4⋊C4).20C6 = C3×C23.41C23φ: C6/C3 → C2 ⊆ Out C2×C4⋊C496(C2xC4:C4).20C6192,1433
(C2×C4⋊C4).21C6 = C12×C4⋊C4φ: trivial image192(C2xC4:C4).21C6192,811
(C2×C4⋊C4).22C6 = Q8×C2×C12φ: trivial image192(C2xC4:C4).22C6192,1405

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