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Extensions 1→N→G→Q→1 with N=C56 and Q=D4

Direct product G=N×Q with N=C56 and Q=D4
dρLabelID
D4×C56224D4xC56448,842

Semidirect products G=N:Q with N=C56 and Q=D4
extensionφ:Q→Aut NdρLabelID
C56⋊1D4 = C8⋊D28φ: D4/C2 → C22 ⊆ Aut C56224C56:1D4448,246
C56⋊2D4 = C56⋊2D4φ: D4/C2 → C22 ⊆ Aut C56224C56:2D4448,668
C56⋊3D4 = C56⋊3D4φ: D4/C2 → C22 ⊆ Aut C56224C56:3D4448,669
C56⋊4D4 = C8⋊7D28φ: D4/C2 → C22 ⊆ Aut C56224C56:4D4448,417
C56⋊5D4 = C56⋊5D4φ: D4/C2 → C22 ⊆ Aut C56224C56:5D4448,685
C56⋊6D4 = C56⋊6D4φ: D4/C2 → C22 ⊆ Aut C56224C56:6D4448,691
C56⋊7D4 = C56⋊7D4φ: D4/C2 → C22 ⊆ Aut C56224C56:7D4448,399
C56⋊8D4 = C56⋊8D4φ: D4/C2 → C22 ⊆ Aut C56224C56:8D4448,708
C56⋊9D4 = C56⋊9D4φ: D4/C2 → C22 ⊆ Aut C56224C56:9D4448,710
C56⋊10D4 = C8⋊3D28φ: D4/C2 → C22 ⊆ Aut C56224C56:10D4448,420
C56⋊11D4 = C56⋊11D4φ: D4/C2 → C22 ⊆ Aut C56224C56:11D4448,688
C56⋊12D4 = C56⋊12D4φ: D4/C2 → C22 ⊆ Aut C56224C56:12D4448,693
C56⋊13D4 = C8⋊8D28φ: D4/C2 → C22 ⊆ Aut C56224C56:13D4448,398
C56⋊14D4 = C56⋊14D4φ: D4/C2 → C22 ⊆ Aut C56224C56:14D4448,705
C56⋊15D4 = C56⋊15D4φ: D4/C2 → C22 ⊆ Aut C56224C56:15D4448,709
C56⋊16D4 = C8⋊9D28φ: D4/C2 → C22 ⊆ Aut C56224C56:16D4448,240
C56⋊17D4 = C56⋊D4φ: D4/C2 → C22 ⊆ Aut C56224C56:17D4448,661
C56⋊18D4 = C56⋊18D4φ: D4/C2 → C22 ⊆ Aut C56224C56:18D4448,662
C56⋊19D4 = C7×C8⋊D4φ: D4/C2 → C22 ⊆ Aut C56224C56:19D4448,876
C56⋊20D4 = C7×C8⋊2D4φ: D4/C2 → C22 ⊆ Aut C56224C56:20D4448,877
C56⋊21D4 = C7×C8⋊3D4φ: D4/C2 → C22 ⊆ Aut C56224C56:21D4448,904
C56⋊22D4 = C28⋊4D8φ: D4/C4 → C2 ⊆ Aut C56224C56:22D4448,229
C56⋊23D4 = C8⋊5D28φ: D4/C4 → C2 ⊆ Aut C56224C56:23D4448,227
C56⋊24D4 = C8×D28φ: D4/C4 → C2 ⊆ Aut C56224C56:24D4448,220
C56⋊25D4 = C8⋊6D28φ: D4/C4 → C2 ⊆ Aut C56224C56:25D4448,222
C56⋊26D4 = C7×C8⋊4D4φ: D4/C4 → C2 ⊆ Aut C56224C56:26D4448,901
C56⋊27D4 = C7×C8⋊5D4φ: D4/C4 → C2 ⊆ Aut C56224C56:27D4448,900
C56⋊28D4 = C7×C8⋊6D4φ: D4/C4 → C2 ⊆ Aut C56224C56:28D4448,844
C56⋊29D4 = C56⋊29D4φ: D4/C22 → C2 ⊆ Aut C56224C56:29D4448,649
C56⋊30D4 = C56⋊30D4φ: D4/C22 → C2 ⊆ Aut C56224C56:30D4448,648
C56⋊31D4 = C8×C7⋊D4φ: D4/C22 → C2 ⊆ Aut C56224C56:31D4448,643
C56⋊32D4 = C56⋊32D4φ: D4/C22 → C2 ⊆ Aut C56224C56:32D4448,645
C56⋊33D4 = C7×C8⋊7D4φ: D4/C22 → C2 ⊆ Aut C56224C56:33D4448,874
C56⋊34D4 = C7×C8⋊8D4φ: D4/C22 → C2 ⊆ Aut C56224C56:34D4448,873
C56⋊35D4 = C7×C8⋊9D4φ: D4/C22 → C2 ⊆ Aut C56224C56:35D4448,843

Non-split extensions G=N.Q with N=C56 and Q=D4
extensionφ:Q→Aut NdρLabelID
C56.1D4 = C8.D28φ: D4/C2 → C22 ⊆ Aut C56224C56.1D4448,249
C56.2D4 = C16⋊D14φ: D4/C2 → C22 ⊆ Aut C561124+C56.2D4448,442
C56.3D4 = C16.D14φ: D4/C2 → C22 ⊆ Aut C562244-C56.3D4448,443
C56.4D4 = C56.4D4φ: D4/C2 → C22 ⊆ Aut C56224C56.4D4448,671
C56.5D4 = C14.D16φ: D4/C2 → C22 ⊆ Aut C56224C56.5D4448,48
C56.6D4 = C56.6D4φ: D4/C2 → C22 ⊆ Aut C56448C56.6D4448,49
C56.7D4 = D56.C4φ: D4/C2 → C22 ⊆ Aut C561124+C56.7D4448,52
C56.8D4 = C56.8D4φ: D4/C2 → C22 ⊆ Aut C562244-C56.8D4448,53
C56.9D4 = C7⋊D32φ: D4/C2 → C22 ⊆ Aut C562244+C56.9D4448,76
C56.10D4 = D16.D7φ: D4/C2 → C22 ⊆ Aut C562244-C56.10D4448,77
C56.11D4 = C7⋊SD64φ: D4/C2 → C22 ⊆ Aut C562244+C56.11D4448,78
C56.12D4 = C7⋊Q64φ: D4/C2 → C22 ⊆ Aut C564484-C56.12D4448,79
C56.13D4 = C14.SD32φ: D4/C2 → C22 ⊆ Aut C56224C56.13D4448,119
C56.14D4 = D8.Dic7φ: D4/C2 → C22 ⊆ Aut C561124C56.14D4448,120
C56.15D4 = C14.Q32φ: D4/C2 → C22 ⊆ Aut C56448C56.15D4448,121
C56.16D4 = Q16.Dic7φ: D4/C2 → C22 ⊆ Aut C562244C56.16D4448,122
C56.17D4 = D14⋊2Q16φ: D4/C2 → C22 ⊆ Aut C56224C56.17D4448,421
C56.18D4 = C8.20D28φ: D4/C2 → C22 ⊆ Aut C562244-C56.18D4448,430
C56.19D4 = C8.21D28φ: D4/C2 → C22 ⊆ Aut C561124+C56.19D4448,431
C56.20D4 = C2×C7⋊D16φ: D4/C2 → C22 ⊆ Aut C56224C56.20D4448,680
C56.21D4 = C2×D8.D7φ: D4/C2 → C22 ⊆ Aut C56224C56.21D4448,682
C56.22D4 = C56.22D4φ: D4/C2 → C22 ⊆ Aut C56224C56.22D4448,689
C56.23D4 = C56.23D4φ: D4/C2 → C22 ⊆ Aut C561124C56.23D4448,694
C56.24D4 = C2×C7⋊SD32φ: D4/C2 → C22 ⊆ Aut C56224C56.24D4448,712
C56.25D4 = C2×C7⋊Q32φ: D4/C2 → C22 ⊆ Aut C56448C56.25D4448,714
C56.26D4 = C56.26D4φ: D4/C2 → C22 ⊆ Aut C56448C56.26D4448,715
C56.27D4 = D14⋊3Q16φ: D4/C2 → C22 ⊆ Aut C56224C56.27D4448,722
C56.28D4 = C56.28D4φ: D4/C2 → C22 ⊆ Aut C56224C56.28D4448,725
C56.29D4 = C56.29D4φ: D4/C2 → C22 ⊆ Aut C562244C56.29D4448,726
C56.30D4 = C8.2D28φ: D4/C2 → C22 ⊆ Aut C56224C56.30D4448,402
C56.31D4 = C56.31D4φ: D4/C2 → C22 ⊆ Aut C56224C56.31D4448,701
C56.32D4 = Q16⋊D14φ: D4/C2 → C22 ⊆ Aut C561124+C56.32D4448,727
C56.33D4 = C56.31C23φ: D4/C2 → C22 ⊆ Aut C562244-C56.33D4448,729
C56.34D4 = D8.D14φ: D4/C2 → C22 ⊆ Aut C561124C56.34D4448,681
C56.35D4 = Q16.D14φ: D4/C2 → C22 ⊆ Aut C562244C56.35D4448,713
C56.36D4 = C56.36D4φ: D4/C2 → C22 ⊆ Aut C56224C56.36D4448,723
C56.37D4 = C56.37D4φ: D4/C2 → C22 ⊆ Aut C56224C56.37D4448,724
C56.38D4 = D56⋊8C4φ: D4/C2 → C22 ⊆ Aut C561124C56.38D4448,45
C56.39D4 = Dic28.C4φ: D4/C2 → C22 ⊆ Aut C562244C56.39D4448,54
C56.40D4 = D8⋊2Dic7φ: D4/C2 → C22 ⊆ Aut C561124C56.40D4448,123
C56.41D4 = C28.58D8φ: D4/C2 → C22 ⊆ Aut C562244C56.41D4448,124
C56.42D4 = C8.24D28φ: D4/C2 → C22 ⊆ Aut C561124C56.42D4448,432
C56.43D4 = C56.43D4φ: D4/C2 → C22 ⊆ Aut C56224C56.43D4448,702
C56.44D4 = C56.44D4φ: D4/C2 → C22 ⊆ Aut C561124C56.44D4448,711
C56.45D4 = C56.30C23φ: D4/C2 → C22 ⊆ Aut C562244C56.45D4448,728
C56.46D4 = M5(2)⋊D7φ: D4/C2 → C22 ⊆ Aut C561124C56.46D4448,71
C56.47D4 = Dic14.C8φ: D4/C2 → C22 ⊆ Aut C562244C56.47D4448,72
C56.48D4 = C56.D4φ: D4/C2 → C22 ⊆ Aut C561124C56.48D4448,110
C56.49D4 = D56⋊4C4φ: D4/C2 → C22 ⊆ Aut C561124C56.49D4448,251
C56.50D4 = C56.50D4φ: D4/C2 → C22 ⊆ Aut C561124C56.50D4448,679
C56.51D4 = C7×C8.D4φ: D4/C2 → C22 ⊆ Aut C56224C56.51D4448,878
C56.52D4 = C7×C8.2D4φ: D4/C2 → C22 ⊆ Aut C56224C56.52D4448,905
C56.53D4 = C7×C16⋊C22φ: D4/C2 → C22 ⊆ Aut C561124C56.53D4448,917
C56.54D4 = C7×Q32⋊C2φ: D4/C2 → C22 ⊆ Aut C562244C56.54D4448,918
C56.55D4 = D224φ: D4/C4 → C2 ⊆ Aut C562242+C56.55D4448,5
C56.56D4 = C224⋊C2φ: D4/C4 → C2 ⊆ Aut C562242C56.56D4448,6
C56.57D4 = Dic112φ: D4/C4 → C2 ⊆ Aut C564482-C56.57D4448,7
C56.58D4 = C8.8D28φ: D4/C4 → C2 ⊆ Aut C56224C56.58D4448,230
C56.59D4 = C28⋊4Q16φ: D4/C4 → C2 ⊆ Aut C56448C56.59D4448,233
C56.60D4 = C2×D112φ: D4/C4 → C2 ⊆ Aut C56224C56.60D4448,436
C56.61D4 = C2×C112⋊C2φ: D4/C4 → C2 ⊆ Aut C56224C56.61D4448,437
C56.62D4 = C2×Dic56φ: D4/C4 → C2 ⊆ Aut C56448C56.62D4448,439
C56.63D4 = D112⋊7C2φ: D4/C4 → C2 ⊆ Aut C562242C56.63D4448,438
C56.64D4 = C28⋊C16φ: D4/C4 → C2 ⊆ Aut C56448C56.64D4448,19
C56.65D4 = C56.16Q8φ: D4/C4 → C2 ⊆ Aut C561122C56.65D4448,20
C56.66D4 = D28.C8φ: D4/C4 → C2 ⊆ Aut C562242C56.66D4448,65
C56.67D4 = D56⋊11C4φ: D4/C4 → C2 ⊆ Aut C561122C56.67D4448,234
C56.68D4 = C7×D32φ: D4/C4 → C2 ⊆ Aut C562242C56.68D4448,175
C56.69D4 = C7×SD64φ: D4/C4 → C2 ⊆ Aut C562242C56.69D4448,176
C56.70D4 = C7×Q64φ: D4/C4 → C2 ⊆ Aut C564482C56.70D4448,177
C56.71D4 = C7×C4⋊Q16φ: D4/C4 → C2 ⊆ Aut C56448C56.71D4448,902
C56.72D4 = C14×D16φ: D4/C4 → C2 ⊆ Aut C56224C56.72D4448,913
C56.73D4 = C14×SD32φ: D4/C4 → C2 ⊆ Aut C56224C56.73D4448,914
C56.74D4 = C14×Q32φ: D4/C4 → C2 ⊆ Aut C56448C56.74D4448,915
C56.75D4 = C7×C8.12D4φ: D4/C4 → C2 ⊆ Aut C56224C56.75D4448,903
C56.76D4 = C7×C4○D16φ: D4/C4 → C2 ⊆ Aut C562242C56.76D4448,916
C56.77D4 = C7×C8○D8φ: D4/C4 → C2 ⊆ Aut C561122C56.77D4448,851
C56.78D4 = C56.78D4φ: D4/C22 → C2 ⊆ Aut C56448C56.78D4448,60
C56.79D4 = C2.D112φ: D4/C22 → C2 ⊆ Aut C56224C56.79D4448,66
C56.80D4 = C28.3D8φ: D4/C22 → C2 ⊆ Aut C561124+C56.80D4448,73
C56.81D4 = C28.4D8φ: D4/C22 → C2 ⊆ Aut C562244-C56.81D4448,74
C56.82D4 = C56.82D4φ: D4/C22 → C2 ⊆ Aut C56224C56.82D4448,650
C56.83D4 = D4.4D28φ: D4/C22 → C2 ⊆ Aut C561124+C56.83D4448,676
C56.84D4 = D4.5D28φ: D4/C22 → C2 ⊆ Aut C562244-C56.84D4448,677
C56.85D4 = D56.1C4φ: D4/C22 → C2 ⊆ Aut C562242C56.85D4448,67
C56.86D4 = D56⋊2C4φ: D4/C22 → C2 ⊆ Aut C561124C56.86D4448,75
C56.87D4 = D4.3D28φ: D4/C22 → C2 ⊆ Aut C561124C56.87D4448,675
C56.88D4 = Dic7⋊C16φ: D4/C22 → C2 ⊆ Aut C56448C56.88D4448,58
C56.89D4 = D14⋊C16φ: D4/C22 → C2 ⊆ Aut C56224C56.89D4448,64
C56.90D4 = C56.9Q8φ: D4/C22 → C2 ⊆ Aut C561124C56.90D4448,68
C56.91D4 = C56.91D4φ: D4/C22 → C2 ⊆ Aut C56224C56.91D4448,106
C56.92D4 = C56.92D4φ: D4/C22 → C2 ⊆ Aut C562244C56.92D4448,118
C56.93D4 = C56.93D4φ: D4/C22 → C2 ⊆ Aut C561124C56.93D4448,678
C56.94D4 = C7×C2.D16φ: D4/C22 → C2 ⊆ Aut C56224C56.94D4448,161
C56.95D4 = C7×C2.Q32φ: D4/C22 → C2 ⊆ Aut C56448C56.95D4448,162
C56.96D4 = C7×M5(2)⋊C2φ: D4/C22 → C2 ⊆ Aut C561124C56.96D4448,165
C56.97D4 = C7×C8.17D4φ: D4/C22 → C2 ⊆ Aut C562244C56.97D4448,166
C56.98D4 = C7×C8.18D4φ: D4/C22 → C2 ⊆ Aut C56224C56.98D4448,875
C56.99D4 = C7×D4.4D4φ: D4/C22 → C2 ⊆ Aut C561124C56.99D4448,880
C56.100D4 = C7×D4.5D4φ: D4/C22 → C2 ⊆ Aut C562244C56.100D4448,881
C56.101D4 = C7×D8.C4φ: D4/C22 → C2 ⊆ Aut C562242C56.101D4448,163
C56.102D4 = C7×D8⋊2C4φ: D4/C22 → C2 ⊆ Aut C561124C56.102D4448,164
C56.103D4 = C7×D4.3D4φ: D4/C22 → C2 ⊆ Aut C561124C56.103D4448,879
C56.104D4 = C7×C23.C8φ: D4/C22 → C2 ⊆ Aut C561124C56.104D4448,153
C56.105D4 = C7×C8.26D4φ: D4/C22 → C2 ⊆ Aut C561124C56.105D4448,852
C56.106D4 = C7×C22⋊C16central extension (φ=1)224C56.106D4448,152
C56.107D4 = C7×D4.C8central extension (φ=1)2242C56.107D4448,154
C56.108D4 = C7×C4⋊C16central extension (φ=1)448C56.108D4448,167
C56.109D4 = C7×C8.C8central extension (φ=1)1122C56.109D4448,168

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