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Extensions 1→N→G→Q→1 with N=C56⋊1C4 and Q=C2

Direct product G=N×Q with N=C56⋊1C4 and Q=C2
dρLabelID
C2×C56⋊1C4448C2xC56:1C4448,639

Semidirect products G=N:Q with N=C56⋊1C4 and Q=C2
extensionφ:Q→Out NdρLabelID
C56⋊1C4⋊1C2 = C2.D112φ: C2/C1 → C2 ⊆ Out C56⋊1C4224C56:1C4:1C2448,66
C56⋊1C4⋊2C2 = C23.35D28φ: C2/C1 → C2 ⊆ Out C56⋊1C4224C56:1C4:2C2448,256
C56⋊1C4⋊3C2 = C23.10D28φ: C2/C1 → C2 ⊆ Out C56⋊1C4224C56:1C4:3C2448,257
C56⋊1C4⋊4C2 = C22.D56φ: C2/C1 → C2 ⊆ Out C56⋊1C4224C56:1C4:4C2448,270
C56⋊1C4⋊5C2 = C23.13D28φ: C2/C1 → C2 ⊆ Out C56⋊1C4224C56:1C4:5C2448,271
C56⋊1C4⋊6C2 = Dic7.D8φ: C2/C1 → C2 ⊆ Out C56⋊1C4224C56:1C4:6C2448,293
C56⋊1C4⋊7C2 = D4.2Dic14φ: C2/C1 → C2 ⊆ Out C56⋊1C4224C56:1C4:7C2448,300
C56⋊1C4⋊8C2 = D14.D8φ: C2/C1 → C2 ⊆ Out C56⋊1C4224C56:1C4:8C2448,308
C56⋊1C4⋊9C2 = C56⋊1C4⋊C2φ: C2/C1 → C2 ⊆ Out C56⋊1C4224C56:1C4:9C2448,318
C56⋊1C4⋊10C2 = D14.Q16φ: C2/C1 → C2 ⊆ Out C56⋊1C4224C56:1C4:10C2448,343
C56⋊1C4⋊11C2 = D14⋊C8.C2φ: C2/C1 → C2 ⊆ Out C56⋊1C4224C56:1C4:11C2448,348
C56⋊1C4⋊12C2 = D28⋊4Q8φ: C2/C1 → C2 ⊆ Out C56⋊1C4224C56:1C4:12C2448,380
C56⋊1C4⋊13C2 = D28.3Q8φ: C2/C1 → C2 ⊆ Out C56⋊1C4224C56:1C4:13C2448,381
C56⋊1C4⋊14C2 = C56⋊29D4φ: C2/C1 → C2 ⊆ Out C56⋊1C4224C56:1C4:14C2448,649
C56⋊1C4⋊15C2 = C56.82D4φ: C2/C1 → C2 ⊆ Out C56⋊1C4224C56:1C4:15C2448,650
C56⋊1C4⋊16C2 = C42.16D14φ: C2/C1 → C2 ⊆ Out C56⋊1C4224C56:1C4:16C2448,244
C56⋊1C4⋊17C2 = C23.47D28φ: C2/C1 → C2 ⊆ Out C56⋊1C4224C56:1C4:17C2448,655
C56⋊1C4⋊18C2 = C56⋊2D4φ: C2/C1 → C2 ⊆ Out C56⋊1C4224C56:1C4:18C2448,668
C56⋊1C4⋊19C2 = C14.SD32φ: C2/C1 → C2 ⊆ Out C56⋊1C4224C56:1C4:19C2448,119
C56⋊1C4⋊20C2 = D7×C2.D8φ: C2/C1 → C2 ⊆ Out C56⋊1C4224C56:1C4:20C2448,413
C56⋊1C4⋊21C2 = C8.27(C4×D7)φ: C2/C1 → C2 ⊆ Out C56⋊1C4224C56:1C4:21C2448,414
C56⋊1C4⋊22C2 = D8×Dic7φ: C2/C1 → C2 ⊆ Out C56⋊1C4224C56:1C4:22C2448,683
C56⋊1C4⋊23C2 = C56⋊6D4φ: C2/C1 → C2 ⊆ Out C56⋊1C4224C56:1C4:23C2448,691
C56⋊1C4⋊24C2 = D14⋊3Q16φ: C2/C1 → C2 ⊆ Out C56⋊1C4224C56:1C4:24C2448,722
C56⋊1C4⋊25C2 = C8⋊(C4×D7)φ: C2/C1 → C2 ⊆ Out C56⋊1C4224C56:1C4:25C2448,395
C56⋊1C4⋊26C2 = SD16⋊Dic7φ: C2/C1 → C2 ⊆ Out C56⋊1C4224C56:1C4:26C2448,698
C56⋊1C4⋊27C2 = C56⋊8D4φ: C2/C1 → C2 ⊆ Out C56⋊1C4224C56:1C4:27C2448,708
C56⋊1C4⋊28C2 = C4×D56φ: trivial image224C56:1C4:28C2448,226
C56⋊1C4⋊29C2 = C23.22D28φ: trivial image224C56:1C4:29C2448,640

Non-split extensions G=N.Q with N=C56⋊1C4 and Q=C2
extensionφ:Q→Out NdρLabelID
C56⋊1C4.1C2 = C56.78D4φ: C2/C1 → C2 ⊆ Out C56⋊1C4448C56:1C4.1C2448,60
C56⋊1C4.2C2 = C112⋊5C4φ: C2/C1 → C2 ⊆ Out C56⋊1C4448C56:1C4.2C2448,61
C56⋊1C4.3C2 = C112⋊6C4φ: C2/C1 → C2 ⊆ Out C56⋊1C4448C56:1C4.3C2448,62
C56⋊1C4.4C2 = C56⋊8Q8φ: C2/C1 → C2 ⊆ Out C56⋊1C4448C56:1C4.4C2448,216
C56⋊1C4.5C2 = C56.13Q8φ: C2/C1 → C2 ⊆ Out C56⋊1C4448C56:1C4.5C2448,217
C56⋊1C4.6C2 = Dic7.Q16φ: C2/C1 → C2 ⊆ Out C56⋊1C4448C56:1C4.6C2448,328
C56⋊1C4.7C2 = Q8.Dic14φ: C2/C1 → C2 ⊆ Out C56⋊1C4448C56:1C4.7C2448,330
C56⋊1C4.8C2 = Dic14.3Q8φ: C2/C1 → C2 ⊆ Out C56⋊1C4448C56:1C4.8C2448,363
C56⋊1C4.9C2 = C28.7Q16φ: C2/C1 → C2 ⊆ Out C56⋊1C4448C56:1C4.9C2448,384
C56⋊1C4.10C2 = C8⋊Dic14φ: C2/C1 → C2 ⊆ Out C56⋊1C4448C56:1C4.10C2448,236
C56⋊1C4.11C2 = C8.4Dic14φ: C2/C1 → C2 ⊆ Out C56⋊1C4448C56:1C4.11C2448,46
C56⋊1C4.12C2 = C8.5Dic14φ: C2/C1 → C2 ⊆ Out C56⋊1C4448C56:1C4.12C2448,47
C56⋊1C4.13C2 = C14.Q32φ: C2/C1 → C2 ⊆ Out C56⋊1C4448C56:1C4.13C2448,121
C56⋊1C4.14C2 = C56⋊2Q8φ: C2/C1 → C2 ⊆ Out C56⋊1C4448C56:1C4.14C2448,408
C56⋊1C4.15C2 = C56.4Q8φ: C2/C1 → C2 ⊆ Out C56⋊1C4448C56:1C4.15C2448,412
C56⋊1C4.16C2 = Q16×Dic7φ: C2/C1 → C2 ⊆ Out C56⋊1C4448C56:1C4.16C2448,717
C56⋊1C4.17C2 = C56⋊3Q8φ: C2/C1 → C2 ⊆ Out C56⋊1C4448C56:1C4.17C2448,390
C56⋊1C4.18C2 = C4×Dic28φ: trivial image448C56:1C4.18C2448,232

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