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

Direct product G=N×Q with N=C56 and Q=C2×C4
dρLabelID
C2×C4×C56448C2xC4xC56448,810

Semidirect products G=N:Q with N=C56 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
C56⋊1(C2×C4) = C42.16D14φ: C2×C4/C2 → C22 ⊆ Aut C56224C56:1(C2xC4)448,244
C56⋊2(C2×C4) = D56⋊C4φ: C2×C4/C2 → C22 ⊆ Aut C56224C56:2(C2xC4)448,245
C56⋊3(C2×C4) = C23.47D28φ: C2×C4/C2 → C22 ⊆ Aut C56224C56:3(C2xC4)448,655
C56⋊4(C2×C4) = Dic7⋊5D8φ: C2×C4/C2 → C22 ⊆ Aut C56224C56:4(C2xC4)448,406
C56⋊5(C2×C4) = D7×C2.D8φ: C2×C4/C2 → C22 ⊆ Aut C56224C56:5(C2xC4)448,413
C56⋊6(C2×C4) = D8×Dic7φ: C2×C4/C2 → C22 ⊆ Aut C56224C56:6(C2xC4)448,683
C56⋊7(C2×C4) = C8⋊(C4×D7)φ: C2×C4/C2 → C22 ⊆ Aut C56224C56:7(C2xC4)448,395
C56⋊8(C2×C4) = D56⋊9C4φ: C2×C4/C2 → C22 ⊆ Aut C56224C56:8(C2xC4)448,403
C56⋊9(C2×C4) = SD16⋊Dic7φ: C2×C4/C2 → C22 ⊆ Aut C56224C56:9(C2xC4)448,698
C56⋊10(C2×C4) = C56⋊(C2×C4)φ: C2×C4/C2 → C22 ⊆ Aut C56224C56:10(C2xC4)448,415
C56⋊11(C2×C4) = C56⋊C2⋊C4φ: C2×C4/C2 → C22 ⊆ Aut C56224C56:11(C2xC4)448,423
C56⋊12(C2×C4) = D8⋊Dic7φ: C2×C4/C2 → C22 ⊆ Aut C56224C56:12(C2xC4)448,686
C56⋊13(C2×C4) = Dic7⋊8SD16φ: C2×C4/C2 → C22 ⊆ Aut C56224C56:13(C2xC4)448,386
C56⋊14(C2×C4) = D7×C4.Q8φ: C2×C4/C2 → C22 ⊆ Aut C56224C56:14(C2xC4)448,393
C56⋊15(C2×C4) = SD16×Dic7φ: C2×C4/C2 → C22 ⊆ Aut C56224C56:15(C2xC4)448,695
C56⋊16(C2×C4) = D7×C8⋊C4φ: C2×C4/C2 → C22 ⊆ Aut C56224C56:16(C2xC4)448,238
C56⋊17(C2×C4) = Dic7.C42φ: C2×C4/C2 → C22 ⊆ Aut C56224C56:17(C2xC4)448,241
C56⋊18(C2×C4) = M4(2)×Dic7φ: C2×C4/C2 → C22 ⊆ Aut C56224C56:18(C2xC4)448,651
C56⋊19(C2×C4) = C7×M4(2)⋊C4φ: C2×C4/C2 → C22 ⊆ Aut C56224C56:19(C2xC4)448,836
C56⋊20(C2×C4) = C7×SD16⋊C4φ: C2×C4/C2 → C22 ⊆ Aut C56224C56:20(C2xC4)448,848
C56⋊21(C2×C4) = C7×D8⋊C4φ: C2×C4/C2 → C22 ⊆ Aut C56224C56:21(C2xC4)448,850
C56⋊22(C2×C4) = C4×D56φ: C2×C4/C4 → C2 ⊆ Aut C56224C56:22(C2xC4)448,226
C56⋊23(C2×C4) = C4×C56⋊C2φ: C2×C4/C4 → C2 ⊆ Aut C56224C56:23(C2xC4)448,225
C56⋊24(C2×C4) = D7×C4×C8φ: C2×C4/C4 → C2 ⊆ Aut C56224C56:24(C2xC4)448,218
C56⋊25(C2×C4) = C4×C8⋊D7φ: C2×C4/C4 → C2 ⊆ Aut C56224C56:25(C2xC4)448,221
C56⋊26(C2×C4) = D8×C28φ: C2×C4/C4 → C2 ⊆ Aut C56224C56:26(C2xC4)448,845
C56⋊27(C2×C4) = SD16×C28φ: C2×C4/C4 → C2 ⊆ Aut C56224C56:27(C2xC4)448,846
C56⋊28(C2×C4) = M4(2)×C28φ: C2×C4/C4 → C2 ⊆ Aut C56224C56:28(C2xC4)448,812
C56⋊29(C2×C4) = C2×C56⋊1C4φ: C2×C4/C22 → C2 ⊆ Aut C56448C56:29(C2xC4)448,639
C56⋊30(C2×C4) = C2×C8⋊Dic7φ: C2×C4/C22 → C2 ⊆ Aut C56448C56:30(C2xC4)448,638
C56⋊31(C2×C4) = C2×C8×Dic7φ: C2×C4/C22 → C2 ⊆ Aut C56448C56:31(C2xC4)448,632
C56⋊32(C2×C4) = C2×C56⋊C4φ: C2×C4/C22 → C2 ⊆ Aut C56448C56:32(C2xC4)448,634
C56⋊33(C2×C4) = C14×C2.D8φ: C2×C4/C22 → C2 ⊆ Aut C56448C56:33(C2xC4)448,834
C56⋊34(C2×C4) = C14×C4.Q8φ: C2×C4/C22 → C2 ⊆ Aut C56448C56:34(C2xC4)448,833
C56⋊35(C2×C4) = C14×C8⋊C4φ: C2×C4/C22 → C2 ⊆ Aut C56448C56:35(C2xC4)448,811

Non-split extensions G=N.Q with N=C56 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
C56.1(C2×C4) = C28.3D8φ: C2×C4/C2 → C22 ⊆ Aut C561124+C56.1(C2xC4)448,73
C56.2(C2×C4) = C28.4D8φ: C2×C4/C2 → C22 ⊆ Aut C562244-C56.2(C2xC4)448,74
C56.3(C2×C4) = D56⋊2C4φ: C2×C4/C2 → C22 ⊆ Aut C561124C56.3(C2xC4)448,75
C56.4(C2×C4) = Dic28⋊C4φ: C2×C4/C2 → C22 ⊆ Aut C56448C56.4(C2xC4)448,250
C56.5(C2×C4) = D56⋊4C4φ: C2×C4/C2 → C22 ⊆ Aut C561124C56.5(C2xC4)448,251
C56.6(C2×C4) = M4(2).Dic7φ: C2×C4/C2 → C22 ⊆ Aut C561124C56.6(C2xC4)448,659
C56.7(C2×C4) = C8.4Dic14φ: C2×C4/C2 → C22 ⊆ Aut C56448C56.7(C2xC4)448,46
C56.8(C2×C4) = C8.5Dic14φ: C2×C4/C2 → C22 ⊆ Aut C56448C56.8(C2xC4)448,47
C56.9(C2×C4) = C14.D16φ: C2×C4/C2 → C22 ⊆ Aut C56224C56.9(C2xC4)448,48
C56.10(C2×C4) = C56.6D4φ: C2×C4/C2 → C22 ⊆ Aut C56448C56.10(C2xC4)448,49
C56.11(C2×C4) = C8.7Dic14φ: C2×C4/C2 → C22 ⊆ Aut C562244C56.11(C2xC4)448,50
C56.12(C2×C4) = Dic28.C4φ: C2×C4/C2 → C22 ⊆ Aut C562244C56.12(C2xC4)448,54
C56.13(C2×C4) = C14.SD32φ: C2×C4/C2 → C22 ⊆ Aut C56224C56.13(C2xC4)448,119
C56.14(C2×C4) = C14.Q32φ: C2×C4/C2 → C22 ⊆ Aut C56448C56.14(C2xC4)448,121
C56.15(C2×C4) = C28.58D8φ: C2×C4/C2 → C22 ⊆ Aut C562244C56.15(C2xC4)448,124
C56.16(C2×C4) = Dic28⋊6C4φ: C2×C4/C2 → C22 ⊆ Aut C56448C56.16(C2xC4)448,407
C56.17(C2×C4) = C8.27(C4×D7)φ: C2×C4/C2 → C22 ⊆ Aut C56224C56.17(C2xC4)448,414
C56.18(C2×C4) = D7×C8.C4φ: C2×C4/C2 → C22 ⊆ Aut C561124C56.18(C2xC4)448,426
C56.19(C2×C4) = Q16×Dic7φ: C2×C4/C2 → C22 ⊆ Aut C56448C56.19(C2xC4)448,717
C56.20(C2×C4) = D8⋊5Dic7φ: C2×C4/C2 → C22 ⊆ Aut C561124C56.20(C2xC4)448,730
C56.21(C2×C4) = D56⋊8C4φ: C2×C4/C2 → C22 ⊆ Aut C561124C56.21(C2xC4)448,45
C56.22(C2×C4) = D56.C4φ: C2×C4/C2 → C22 ⊆ Aut C561124+C56.22(C2xC4)448,52
C56.23(C2×C4) = C56.8D4φ: C2×C4/C2 → C22 ⊆ Aut C562244-C56.23(C2xC4)448,53
C56.24(C2×C4) = Dic28⋊9C4φ: C2×C4/C2 → C22 ⊆ Aut C56448C56.24(C2xC4)448,387
C56.25(C2×C4) = D8.Dic7φ: C2×C4/C2 → C22 ⊆ Aut C561124C56.25(C2xC4)448,120
C56.26(C2×C4) = Q16.Dic7φ: C2×C4/C2 → C22 ⊆ Aut C562244C56.26(C2xC4)448,122
C56.27(C2×C4) = D8⋊2Dic7φ: C2×C4/C2 → C22 ⊆ Aut C561124C56.27(C2xC4)448,123
C56.28(C2×C4) = M4(2).25D14φ: C2×C4/C2 → C22 ⊆ Aut C561124C56.28(C2xC4)448,427
C56.29(C2×C4) = D56⋊10C4φ: C2×C4/C2 → C22 ⊆ Aut C561124C56.29(C2xC4)448,428
C56.30(C2×C4) = Q16⋊Dic7φ: C2×C4/C2 → C22 ⊆ Aut C56448C56.30(C2xC4)448,718
C56.31(C2×C4) = D8⋊4Dic7φ: C2×C4/C2 → C22 ⊆ Aut C561124C56.31(C2xC4)448,731
C56.32(C2×C4) = C56.Q8φ: C2×C4/C2 → C22 ⊆ Aut C561124C56.32(C2xC4)448,44
C56.33(C2×C4) = C8.Dic14φ: C2×C4/C2 → C22 ⊆ Aut C561124C56.33(C2xC4)448,51
C56.34(C2×C4) = (C8×D7)⋊C4φ: C2×C4/C2 → C22 ⊆ Aut C56224C56.34(C2xC4)448,394
C56.35(C2×C4) = D56⋊7C4φ: C2×C4/C2 → C22 ⊆ Aut C561124C56.35(C2xC4)448,429
C56.36(C2×C4) = C28.15C42φ: C2×C4/C2 → C22 ⊆ Aut C561124C56.36(C2xC4)448,23
C56.37(C2×C4) = D14.4C42φ: C2×C4/C2 → C22 ⊆ Aut C56224C56.37(C2xC4)448,242
C56.38(C2×C4) = D7×M5(2)φ: C2×C4/C2 → C22 ⊆ Aut C561124C56.38(C2xC4)448,440
C56.39(C2×C4) = C16.12D14φ: C2×C4/C2 → C22 ⊆ Aut C562244C56.39(C2xC4)448,441
C56.40(C2×C4) = C28.7C42φ: C2×C4/C2 → C22 ⊆ Aut C56224C56.40(C2xC4)448,656
C56.41(C2×C4) = C56.70C23φ: C2×C4/C2 → C22 ⊆ Aut C562244C56.41(C2xC4)448,674
C56.42(C2×C4) = C7×D8⋊2C4φ: C2×C4/C2 → C22 ⊆ Aut C561124C56.42(C2xC4)448,164
C56.43(C2×C4) = C7×M5(2)⋊C2φ: C2×C4/C2 → C22 ⊆ Aut C561124C56.43(C2xC4)448,165
C56.44(C2×C4) = C7×C8.17D4φ: C2×C4/C2 → C22 ⊆ Aut C562244C56.44(C2xC4)448,166
C56.45(C2×C4) = C7×M4(2).C4φ: C2×C4/C2 → C22 ⊆ Aut C561124C56.45(C2xC4)448,838
C56.46(C2×C4) = C7×Q16⋊C4φ: C2×C4/C2 → C22 ⊆ Aut C56448C56.46(C2xC4)448,849
C56.47(C2×C4) = C7×C8.26D4φ: C2×C4/C2 → C22 ⊆ Aut C561124C56.47(C2xC4)448,852
C56.48(C2×C4) = C56.78D4φ: C2×C4/C4 → C2 ⊆ Aut C56448C56.48(C2xC4)448,60
C56.49(C2×C4) = C2.D112φ: C2×C4/C4 → C2 ⊆ Aut C56224C56.49(C2xC4)448,66
C56.50(C2×C4) = D56.1C4φ: C2×C4/C4 → C2 ⊆ Aut C562242C56.50(C2xC4)448,67
C56.51(C2×C4) = C4×Dic28φ: C2×C4/C4 → C2 ⊆ Aut C56448C56.51(C2xC4)448,232
C56.52(C2×C4) = D56⋊11C4φ: C2×C4/C4 → C2 ⊆ Aut C561122C56.52(C2xC4)448,234
C56.53(C2×C4) = D7×C32φ: C2×C4/C4 → C2 ⊆ Aut C562242C56.53(C2xC4)448,3
C56.54(C2×C4) = C32⋊D7φ: C2×C4/C4 → C2 ⊆ Aut C562242C56.54(C2xC4)448,4
C56.55(C2×C4) = C4×C7⋊C16φ: C2×C4/C4 → C2 ⊆ Aut C56448C56.55(C2xC4)448,17
C56.56(C2×C4) = C56.C8φ: C2×C4/C4 → C2 ⊆ Aut C56448C56.56(C2xC4)448,18
C56.57(C2×C4) = C16×Dic7φ: C2×C4/C4 → C2 ⊆ Aut C56448C56.57(C2xC4)448,57
C56.58(C2×C4) = C112⋊9C4φ: C2×C4/C4 → C2 ⊆ Aut C56448C56.58(C2xC4)448,59
C56.59(C2×C4) = D14.C42φ: C2×C4/C4 → C2 ⊆ Aut C56224C56.59(C2xC4)448,223
C56.60(C2×C4) = D7×C2×C16φ: C2×C4/C4 → C2 ⊆ Aut C56224C56.60(C2xC4)448,433
C56.61(C2×C4) = C2×C16⋊D7φ: C2×C4/C4 → C2 ⊆ Aut C56224C56.61(C2xC4)448,434
C56.62(C2×C4) = D28.4C8φ: C2×C4/C4 → C2 ⊆ Aut C562242C56.62(C2xC4)448,435
C56.63(C2×C4) = C7×C2.D16φ: C2×C4/C4 → C2 ⊆ Aut C56224C56.63(C2xC4)448,161
C56.64(C2×C4) = C7×C2.Q32φ: C2×C4/C4 → C2 ⊆ Aut C56448C56.64(C2xC4)448,162
C56.65(C2×C4) = C7×D8.C4φ: C2×C4/C4 → C2 ⊆ Aut C562242C56.65(C2xC4)448,163
C56.66(C2×C4) = Q16×C28φ: C2×C4/C4 → C2 ⊆ Aut C56448C56.66(C2xC4)448,847
C56.67(C2×C4) = C7×C8○D8φ: C2×C4/C4 → C2 ⊆ Aut C561122C56.67(C2xC4)448,851
C56.68(C2×C4) = C7×D4○C16φ: C2×C4/C4 → C2 ⊆ Aut C562242C56.68(C2xC4)448,912
C56.69(C2×C4) = C112⋊5C4φ: C2×C4/C22 → C2 ⊆ Aut C56448C56.69(C2xC4)448,61
C56.70(C2×C4) = C112⋊6C4φ: C2×C4/C22 → C2 ⊆ Aut C56448C56.70(C2xC4)448,62
C56.71(C2×C4) = C112.C4φ: C2×C4/C22 → C2 ⊆ Aut C562242C56.71(C2xC4)448,63
C56.72(C2×C4) = C16⋊Dic7φ: C2×C4/C22 → C2 ⊆ Aut C561124C56.72(C2xC4)448,70
C56.73(C2×C4) = C23.22D28φ: C2×C4/C22 → C2 ⊆ Aut C56224C56.73(C2xC4)448,640
C56.74(C2×C4) = C2×C56.C4φ: C2×C4/C22 → C2 ⊆ Aut C56224C56.74(C2xC4)448,641
C56.75(C2×C4) = C2×C7⋊C32φ: C2×C4/C22 → C2 ⊆ Aut C56448C56.75(C2xC4)448,55
C56.76(C2×C4) = C7⋊M6(2)φ: C2×C4/C22 → C2 ⊆ Aut C562242C56.76(C2xC4)448,56
C56.77(C2×C4) = C112⋊C4φ: C2×C4/C22 → C2 ⊆ Aut C561124C56.77(C2xC4)448,69
C56.78(C2×C4) = C22×C7⋊C16φ: C2×C4/C22 → C2 ⊆ Aut C56448C56.78(C2xC4)448,630
C56.79(C2×C4) = C2×C28.C8φ: C2×C4/C22 → C2 ⊆ Aut C56224C56.79(C2xC4)448,631
C56.80(C2×C4) = C28.12C42φ: C2×C4/C22 → C2 ⊆ Aut C56224C56.80(C2xC4)448,635
C56.81(C2×C4) = C7×C16⋊3C4φ: C2×C4/C22 → C2 ⊆ Aut C56448C56.81(C2xC4)448,170
C56.82(C2×C4) = C7×C16⋊4C4φ: C2×C4/C22 → C2 ⊆ Aut C56448C56.82(C2xC4)448,171
C56.83(C2×C4) = C7×C8.4Q8φ: C2×C4/C22 → C2 ⊆ Aut C562242C56.83(C2xC4)448,172
C56.84(C2×C4) = C7×C23.25D4φ: C2×C4/C22 → C2 ⊆ Aut C56224C56.84(C2xC4)448,835
C56.85(C2×C4) = C14×C8.C4φ: C2×C4/C22 → C2 ⊆ Aut C56224C56.85(C2xC4)448,837
C56.86(C2×C4) = C7×C8.Q8φ: C2×C4/C22 → C2 ⊆ Aut C561124C56.86(C2xC4)448,169
C56.87(C2×C4) = C7×C16⋊C4φ: C2×C4/C22 → C2 ⊆ Aut C561124C56.87(C2xC4)448,151
C56.88(C2×C4) = C7×C8○2M4(2)φ: C2×C4/C22 → C2 ⊆ Aut C56224C56.88(C2xC4)448,813
C56.89(C2×C4) = C14×M5(2)φ: C2×C4/C22 → C2 ⊆ Aut C56224C56.89(C2xC4)448,911
C56.90(C2×C4) = C7×C16⋊5C4central extension (φ=1)448C56.90(C2xC4)448,150
C56.91(C2×C4) = C7×M6(2)central extension (φ=1)2242C56.91(C2xC4)448,174

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