Extensions 1→N→G→Q→1 with N=C2×C4⋊C4 and Q=C14

Direct product G=N×Q with N=C2×C4⋊C4 and Q=C14
dρLabelID
C4⋊C4×C2×C14448C4:C4xC2xC14448,1296

Semidirect products G=N:Q with N=C2×C4⋊C4 and Q=C14
extensionφ:Q→Out NdρLabelID
(C2×C4⋊C4)⋊1C14 = C7×C23.7Q8φ: C14/C7C2 ⊆ Out C2×C4⋊C4224(C2xC4:C4):1C14448,788
(C2×C4⋊C4)⋊2C14 = C7×C23.8Q8φ: C14/C7C2 ⊆ Out C2×C4⋊C4224(C2xC4:C4):2C14448,793
(C2×C4⋊C4)⋊3C14 = C7×C24.C22φ: C14/C7C2 ⊆ Out C2×C4⋊C4224(C2xC4:C4):3C14448,796
(C2×C4⋊C4)⋊4C14 = C7×C24.3C22φ: C14/C7C2 ⊆ Out C2×C4⋊C4224(C2xC4:C4):4C14448,798
(C2×C4⋊C4)⋊5C14 = C7×C23.10D4φ: C14/C7C2 ⊆ Out C2×C4⋊C4224(C2xC4:C4):5C14448,802
(C2×C4⋊C4)⋊6C14 = C7×C23.Q8φ: C14/C7C2 ⊆ Out C2×C4⋊C4224(C2xC4:C4):6C14448,804
(C2×C4⋊C4)⋊7C14 = C7×C23.11D4φ: C14/C7C2 ⊆ Out C2×C4⋊C4224(C2xC4:C4):7C14448,805
(C2×C4⋊C4)⋊8C14 = C7×C23.4Q8φ: C14/C7C2 ⊆ Out C2×C4⋊C4224(C2xC4:C4):8C14448,807
(C2×C4⋊C4)⋊9C14 = C14×D4⋊C4φ: C14/C7C2 ⊆ Out C2×C4⋊C4224(C2xC4:C4):9C14448,822
(C2×C4⋊C4)⋊10C14 = C7×C23.36D4φ: C14/C7C2 ⊆ Out C2×C4⋊C4224(C2xC4:C4):10C14448,825
(C2×C4⋊C4)⋊11C14 = C7×C22.D8φ: C14/C7C2 ⊆ Out C2×C4⋊C4224(C2xC4:C4):11C14448,888
(C2×C4⋊C4)⋊12C14 = C7×C23.46D4φ: C14/C7C2 ⊆ Out C2×C4⋊C4224(C2xC4:C4):12C14448,889
(C2×C4⋊C4)⋊13C14 = C7×C23.33C23φ: C14/C7C2 ⊆ Out C2×C4⋊C4224(C2xC4:C4):13C14448,1303
(C2×C4⋊C4)⋊14C14 = C14×C4⋊D4φ: C14/C7C2 ⊆ Out C2×C4⋊C4224(C2xC4:C4):14C14448,1305
(C2×C4⋊C4)⋊15C14 = C14×C22⋊Q8φ: C14/C7C2 ⊆ Out C2×C4⋊C4224(C2xC4:C4):15C14448,1306
(C2×C4⋊C4)⋊16C14 = C14×C22.D4φ: C14/C7C2 ⊆ Out C2×C4⋊C4224(C2xC4:C4):16C14448,1307
(C2×C4⋊C4)⋊17C14 = C14×C422C2φ: C14/C7C2 ⊆ Out C2×C4⋊C4224(C2xC4:C4):17C14448,1311
(C2×C4⋊C4)⋊18C14 = C7×C22.31C24φ: C14/C7C2 ⊆ Out C2×C4⋊C4224(C2xC4:C4):18C14448,1320
(C2×C4⋊C4)⋊19C14 = C7×C22.33C24φ: C14/C7C2 ⊆ Out C2×C4⋊C4224(C2xC4:C4):19C14448,1322
(C2×C4⋊C4)⋊20C14 = C7×D46D4φ: C14/C7C2 ⊆ Out C2×C4⋊C4224(C2xC4:C4):20C14448,1330
(C2×C4⋊C4)⋊21C14 = C7×C22.46C24φ: C14/C7C2 ⊆ Out C2×C4⋊C4224(C2xC4:C4):21C14448,1335
(C2×C4⋊C4)⋊22C14 = C7×C22.47C24φ: C14/C7C2 ⊆ Out C2×C4⋊C4224(C2xC4:C4):22C14448,1336
(C2×C4⋊C4)⋊23C14 = C7×D43Q8φ: C14/C7C2 ⊆ Out C2×C4⋊C4224(C2xC4:C4):23C14448,1337
(C2×C4⋊C4)⋊24C14 = C14×C42⋊C2φ: trivial image224(C2xC4:C4):24C14448,1297
(C2×C4⋊C4)⋊25C14 = D4×C2×C28φ: trivial image224(C2xC4:C4):25C14448,1298

Non-split extensions G=N.Q with N=C2×C4⋊C4 and Q=C14
extensionφ:Q→Out NdρLabelID
(C2×C4⋊C4).1C14 = C7×C22.M4(2)φ: C14/C7C2 ⊆ Out C2×C4⋊C4224(C2xC4:C4).1C14448,128
(C2×C4⋊C4).2C14 = C7×C22.4Q16φ: C14/C7C2 ⊆ Out C2×C4⋊C4448(C2xC4:C4).2C14448,144
(C2×C4⋊C4).3C14 = C7×C22.C42φ: C14/C7C2 ⊆ Out C2×C4⋊C4224(C2xC4:C4).3C14448,147
(C2×C4⋊C4).4C14 = C7×C428C4φ: C14/C7C2 ⊆ Out C2×C4⋊C4448(C2xC4:C4).4C14448,790
(C2×C4⋊C4).5C14 = C7×C429C4φ: C14/C7C2 ⊆ Out C2×C4⋊C4448(C2xC4:C4).5C14448,792
(C2×C4⋊C4).6C14 = C7×C23.63C23φ: C14/C7C2 ⊆ Out C2×C4⋊C4448(C2xC4:C4).6C14448,795
(C2×C4⋊C4).7C14 = C7×C23.65C23φ: C14/C7C2 ⊆ Out C2×C4⋊C4448(C2xC4:C4).7C14448,797
(C2×C4⋊C4).8C14 = C7×C23.67C23φ: C14/C7C2 ⊆ Out C2×C4⋊C4448(C2xC4:C4).8C14448,799
(C2×C4⋊C4).9C14 = C7×C23.78C23φ: C14/C7C2 ⊆ Out C2×C4⋊C4448(C2xC4:C4).9C14448,803
(C2×C4⋊C4).10C14 = C7×C23.81C23φ: C14/C7C2 ⊆ Out C2×C4⋊C4448(C2xC4:C4).10C14448,806
(C2×C4⋊C4).11C14 = C7×C23.83C23φ: C14/C7C2 ⊆ Out C2×C4⋊C4448(C2xC4:C4).11C14448,808
(C2×C4⋊C4).12C14 = C14×Q8⋊C4φ: C14/C7C2 ⊆ Out C2×C4⋊C4448(C2xC4:C4).12C14448,823
(C2×C4⋊C4).13C14 = C14×C4.Q8φ: C14/C7C2 ⊆ Out C2×C4⋊C4448(C2xC4:C4).13C14448,833
(C2×C4⋊C4).14C14 = C14×C2.D8φ: C14/C7C2 ⊆ Out C2×C4⋊C4448(C2xC4:C4).14C14448,834
(C2×C4⋊C4).15C14 = C7×M4(2)⋊C4φ: C14/C7C2 ⊆ Out C2×C4⋊C4224(C2xC4:C4).15C14448,836
(C2×C4⋊C4).16C14 = C7×C23.47D4φ: C14/C7C2 ⊆ Out C2×C4⋊C4224(C2xC4:C4).16C14448,891
(C2×C4⋊C4).17C14 = C7×C23.48D4φ: C14/C7C2 ⊆ Out C2×C4⋊C4224(C2xC4:C4).17C14448,892
(C2×C4⋊C4).18C14 = C14×C42.C2φ: C14/C7C2 ⊆ Out C2×C4⋊C4448(C2xC4:C4).18C14448,1310
(C2×C4⋊C4).19C14 = C14×C4⋊Q8φ: C14/C7C2 ⊆ Out C2×C4⋊C4448(C2xC4:C4).19C14448,1314
(C2×C4⋊C4).20C14 = C7×C23.41C23φ: C14/C7C2 ⊆ Out C2×C4⋊C4224(C2xC4:C4).20C14448,1327
(C2×C4⋊C4).21C14 = C4⋊C4×C28φ: trivial image448(C2xC4:C4).21C14448,786
(C2×C4⋊C4).22C14 = Q8×C2×C28φ: trivial image448(C2xC4:C4).22C14448,1299

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