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Extensions 1→N→G→Q→1 with N=C2×C56⋊C2 and Q=C2

Direct product G=N×Q with N=C2×C56⋊C2 and Q=C2
dρLabelID
C22×C56⋊C2224C2^2xC56:C2448,1192

Semidirect products G=N:Q with N=C2×C56⋊C2 and Q=C2
extensionφ:Q→Out NdρLabelID
(C2×C56⋊C2)⋊1C2 = C8⋊D28φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2):1C2448,246
(C2×C56⋊C2)⋊2C2 = C56⋊2D4φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2):2C2448,668
(C2×C56⋊C2)⋊3C2 = D4.3D28φ: C2/C1 → C2 ⊆ Out C2×C56⋊C21124(C2xC56:C2):3C2448,675
(C2×C56⋊C2)⋊4C2 = C2×C8⋊D14φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2112(C2xC56:C2):4C2448,1199
(C2×C56⋊C2)⋊5C2 = C2×C8.D14φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2):5C2448,1200
(C2×C56⋊C2)⋊6C2 = D4.11D28φ: C2/C1 → C2 ⊆ Out C2×C56⋊C21124(C2xC56:C2):6C2448,1204
(C2×C56⋊C2)⋊7C2 = C8⋊5D28φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2):7C2448,227
(C2×C56⋊C2)⋊8C2 = C8.8D28φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2):8C2448,230
(C2×C56⋊C2)⋊9C2 = D28.31D4φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2112(C2xC56:C2):9C2448,265
(C2×C56⋊C2)⋊10C2 = D28.32D4φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2):10C2448,267
(C2×C56⋊C2)⋊11C2 = D28⋊14D4φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2):11C2448,268
(C2×C56⋊C2)⋊12C2 = Dic14⋊14D4φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2):12C2448,272
(C2×C56⋊C2)⋊13C2 = Dic14⋊2D4φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2):13C2448,296
(C2×C56⋊C2)⋊14C2 = D4.6D28φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2112(C2xC56:C2):14C2448,310
(C2×C56⋊C2)⋊15C2 = D4⋊3D28φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2):15C2448,315
(C2×C56⋊C2)⋊16C2 = D28.D4φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2):16C2448,321
(C2×C56⋊C2)⋊17C2 = Q8⋊2D28φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2):17C2448,340
(C2×C56⋊C2)⋊18C2 = Q8.D28φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2):18C2448,344
(C2×C56⋊C2)⋊19C2 = D28.19D4φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2):19C2448,378
(C2×C56⋊C2)⋊20C2 = Dic14⋊8D4φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2):20C2448,382
(C2×C56⋊C2)⋊21C2 = C56⋊30D4φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2):21C2448,648
(C2×C56⋊C2)⋊22C2 = C8⋊3D28φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2):22C2448,420
(C2×C56⋊C2)⋊23C2 = C56⋊11D4φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2):23C2448,688
(C2×C56⋊C2)⋊24C2 = C2×D8⋊D7φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2112(C2xC56:C2):24C2448,1208
(C2×C56⋊C2)⋊25C2 = C2×Q16⋊D7φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2):25C2448,1217
(C2×C56⋊C2)⋊26C2 = C8.24D28φ: C2/C1 → C2 ⊆ Out C2×C56⋊C21124(C2xC56:C2):26C2448,432
(C2×C56⋊C2)⋊27C2 = D8⋊11D14φ: C2/C1 → C2 ⊆ Out C2×C56⋊C21124(C2xC56:C2):27C2448,1223
(C2×C56⋊C2)⋊28C2 = C8⋊8D28φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2):28C2448,398
(C2×C56⋊C2)⋊29C2 = C56.43D4φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2):29C2448,702
(C2×C56⋊C2)⋊30C2 = C56⋊15D4φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2):30C2448,709
(C2×C56⋊C2)⋊31C2 = C2×D7×SD16φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2112(C2xC56:C2):31C2448,1211
(C2×C56⋊C2)⋊32C2 = C2×SD16⋊3D7φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2):32C2448,1214
(C2×C56⋊C2)⋊33C2 = C2×D56⋊7C2φ: trivial image224(C2xC56:C2):33C2448,1194

Non-split extensions G=N.Q with N=C2×C56⋊C2 and Q=C2
extensionφ:Q→Out NdρLabelID
(C2×C56⋊C2).1C2 = C42.16D14φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2).1C2448,244
(C2×C56⋊C2).2C2 = C8.D28φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2).2C2448,249
(C2×C56⋊C2).3C2 = Dic14.11D4φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2).3C2448,332
(C2×C56⋊C2).4C2 = Dic7⋊SD16φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2).4C2448,352
(C2×C56⋊C2).5C2 = C28⋊SD16φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2).5C2448,375
(C2×C56⋊C2).6C2 = C42.36D14φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2).6C2448,379
(C2×C56⋊C2).7C2 = C56⋊C2⋊C4φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2).7C2448,423
(C2×C56⋊C2).8C2 = C56.37D4φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2).8C2448,724
(C2×C56⋊C2).9C2 = Dic7⋊8SD16φ: C2/C1 → C2 ⊆ Out C2×C56⋊C2224(C2xC56:C2).9C2448,386
(C2×C56⋊C2).10C2 = C4×C56⋊C2φ: trivial image224(C2xC56:C2).10C2448,225

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