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Extensions 1→N→G→Q→1 with N=C8 and Q=C7⋊D4

Direct product G=N×Q with N=C8 and Q=C7⋊D4
dρLabelID
C8×C7⋊D4224C8xC7:D4448,643

Semidirect products G=N:Q with N=C8 and Q=C7⋊D4
extensionφ:Q→Aut NdρLabelID
C8⋊1(C7⋊D4) = C56⋊2D4φ: C7⋊D4/C14 → C22 ⊆ Aut C8224C8:1(C7:D4)448,668
C8⋊2(C7⋊D4) = C56⋊3D4φ: C7⋊D4/C14 → C22 ⊆ Aut C8224C8:2(C7:D4)448,669
C8⋊3(C7⋊D4) = C56⋊11D4φ: C7⋊D4/C14 → C22 ⊆ Aut C8224C8:3(C7:D4)448,688
C8⋊4(C7⋊D4) = C56⋊12D4φ: C7⋊D4/C14 → C22 ⊆ Aut C8224C8:4(C7:D4)448,693
C8⋊5(C7⋊D4) = C56⋊8D4φ: C7⋊D4/C14 → C22 ⊆ Aut C8224C8:5(C7:D4)448,708
C8⋊6(C7⋊D4) = C56⋊9D4φ: C7⋊D4/C14 → C22 ⊆ Aut C8224C8:6(C7:D4)448,710
C8⋊7(C7⋊D4) = C56⋊5D4φ: C7⋊D4/Dic7 → C2 ⊆ Aut C8224C8:7(C7:D4)448,685
C8⋊8(C7⋊D4) = C56⋊15D4φ: C7⋊D4/Dic7 → C2 ⊆ Aut C8224C8:8(C7:D4)448,709
C8⋊9(C7⋊D4) = C56⋊18D4φ: C7⋊D4/Dic7 → C2 ⊆ Aut C8224C8:9(C7:D4)448,662
C8⋊10(C7⋊D4) = C56⋊6D4φ: C7⋊D4/D14 → C2 ⊆ Aut C8224C8:10(C7:D4)448,691
C8⋊11(C7⋊D4) = C56⋊14D4φ: C7⋊D4/D14 → C2 ⊆ Aut C8224C8:11(C7:D4)448,705
C8⋊12(C7⋊D4) = C56⋊D4φ: C7⋊D4/D14 → C2 ⊆ Aut C8224C8:12(C7:D4)448,661
C8⋊13(C7⋊D4) = C56⋊29D4φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C8224C8:13(C7:D4)448,649
C8⋊14(C7⋊D4) = C56⋊30D4φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C8224C8:14(C7:D4)448,648
C8⋊15(C7⋊D4) = C56⋊32D4φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C8224C8:15(C7:D4)448,645

Non-split extensions G=N.Q with N=C8 and Q=C7⋊D4
extensionφ:Q→Aut NdρLabelID
C8.1(C7⋊D4) = C56.4D4φ: C7⋊D4/C14 → C22 ⊆ Aut C8224C8.1(C7:D4)448,671
C8.2(C7⋊D4) = D8.D14φ: C7⋊D4/C14 → C22 ⊆ Aut C81124C8.2(C7:D4)448,681
C8.3(C7⋊D4) = C56.31D4φ: C7⋊D4/C14 → C22 ⊆ Aut C8224C8.3(C7:D4)448,701
C8.4(C7⋊D4) = Q16.D14φ: C7⋊D4/C14 → C22 ⊆ Aut C82244C8.4(C7:D4)448,713
C8.5(C7⋊D4) = C56.36D4φ: C7⋊D4/C14 → C22 ⊆ Aut C8224C8.5(C7:D4)448,723
C8.6(C7⋊D4) = C56.37D4φ: C7⋊D4/C14 → C22 ⊆ Aut C8224C8.6(C7:D4)448,724
C8.7(C7⋊D4) = Q16⋊D14φ: C7⋊D4/C14 → C22 ⊆ Aut C81124+C8.7(C7:D4)448,727
C8.8(C7⋊D4) = C56.31C23φ: C7⋊D4/C14 → C22 ⊆ Aut C82244-C8.8(C7:D4)448,729
C8.9(C7⋊D4) = C7⋊D32φ: C7⋊D4/Dic7 → C2 ⊆ Aut C82244+C8.9(C7:D4)448,76
C8.10(C7⋊D4) = D16.D7φ: C7⋊D4/Dic7 → C2 ⊆ Aut C82244-C8.10(C7:D4)448,77
C8.11(C7⋊D4) = C7⋊SD64φ: C7⋊D4/Dic7 → C2 ⊆ Aut C82244+C8.11(C7:D4)448,78
C8.12(C7⋊D4) = C7⋊Q64φ: C7⋊D4/Dic7 → C2 ⊆ Aut C84484-C8.12(C7:D4)448,79
C8.13(C7⋊D4) = C2×C7⋊D16φ: C7⋊D4/Dic7 → C2 ⊆ Aut C8224C8.13(C7:D4)448,680
C8.14(C7⋊D4) = C2×D8.D7φ: C7⋊D4/Dic7 → C2 ⊆ Aut C8224C8.14(C7:D4)448,682
C8.15(C7⋊D4) = C56.22D4φ: C7⋊D4/Dic7 → C2 ⊆ Aut C8224C8.15(C7:D4)448,689
C8.16(C7⋊D4) = C2×C7⋊SD32φ: C7⋊D4/Dic7 → C2 ⊆ Aut C8224C8.16(C7:D4)448,712
C8.17(C7⋊D4) = C2×C7⋊Q32φ: C7⋊D4/Dic7 → C2 ⊆ Aut C8448C8.17(C7:D4)448,714
C8.18(C7⋊D4) = C56.26D4φ: C7⋊D4/Dic7 → C2 ⊆ Aut C8448C8.18(C7:D4)448,715
C8.19(C7⋊D4) = C56.28D4φ: C7⋊D4/Dic7 → C2 ⊆ Aut C8224C8.19(C7:D4)448,725
C8.20(C7⋊D4) = C56.43D4φ: C7⋊D4/Dic7 → C2 ⊆ Aut C8224C8.20(C7:D4)448,702
C8.21(C7⋊D4) = C56.30C23φ: C7⋊D4/Dic7 → C2 ⊆ Aut C82244C8.21(C7:D4)448,728
C8.22(C7⋊D4) = C56.93D4φ: C7⋊D4/Dic7 → C2 ⊆ Aut C81124C8.22(C7:D4)448,678
C8.23(C7⋊D4) = C14.SD32φ: C7⋊D4/D14 → C2 ⊆ Aut C8224C8.23(C7:D4)448,119
C8.24(C7⋊D4) = D8.Dic7φ: C7⋊D4/D14 → C2 ⊆ Aut C81124C8.24(C7:D4)448,120
C8.25(C7⋊D4) = C14.Q32φ: C7⋊D4/D14 → C2 ⊆ Aut C8448C8.25(C7:D4)448,121
C8.26(C7⋊D4) = Q16.Dic7φ: C7⋊D4/D14 → C2 ⊆ Aut C82244C8.26(C7:D4)448,122
C8.27(C7⋊D4) = C56.23D4φ: C7⋊D4/D14 → C2 ⊆ Aut C81124C8.27(C7:D4)448,694
C8.28(C7⋊D4) = D14⋊3Q16φ: C7⋊D4/D14 → C2 ⊆ Aut C8224C8.28(C7:D4)448,722
C8.29(C7⋊D4) = C56.29D4φ: C7⋊D4/D14 → C2 ⊆ Aut C82244C8.29(C7:D4)448,726
C8.30(C7⋊D4) = D8⋊2Dic7φ: C7⋊D4/D14 → C2 ⊆ Aut C81124C8.30(C7:D4)448,123
C8.31(C7⋊D4) = C28.58D8φ: C7⋊D4/D14 → C2 ⊆ Aut C82244C8.31(C7:D4)448,124
C8.32(C7⋊D4) = C56.44D4φ: C7⋊D4/D14 → C2 ⊆ Aut C81124C8.32(C7:D4)448,711
C8.33(C7⋊D4) = C56.D4φ: C7⋊D4/D14 → C2 ⊆ Aut C81124C8.33(C7:D4)448,110
C8.34(C7⋊D4) = C56.92D4φ: C7⋊D4/D14 → C2 ⊆ Aut C82244C8.34(C7:D4)448,118
C8.35(C7⋊D4) = C56.78D4φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C8448C8.35(C7:D4)448,60
C8.36(C7⋊D4) = C2.D112φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C8224C8.36(C7:D4)448,66
C8.37(C7⋊D4) = C28.3D8φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C81124+C8.37(C7:D4)448,73
C8.38(C7⋊D4) = C28.4D8φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C82244-C8.38(C7:D4)448,74
C8.39(C7⋊D4) = C56.82D4φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C8224C8.39(C7:D4)448,650
C8.40(C7⋊D4) = D4.4D28φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C81124+C8.40(C7:D4)448,676
C8.41(C7⋊D4) = D4.5D28φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C82244-C8.41(C7:D4)448,677
C8.42(C7⋊D4) = D56.1C4φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C82242C8.42(C7:D4)448,67
C8.43(C7⋊D4) = D56⋊2C4φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C81124C8.43(C7:D4)448,75
C8.44(C7⋊D4) = D4.3D28φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C81124C8.44(C7:D4)448,675
C8.45(C7⋊D4) = D28.C8φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C82242C8.45(C7:D4)448,65
C8.46(C7⋊D4) = M5(2)⋊D7φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C81124C8.46(C7:D4)448,71
C8.47(C7⋊D4) = C56.50D4φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C81124C8.47(C7:D4)448,679
C8.48(C7⋊D4) = Dic7⋊C16central extension (φ=1)448C8.48(C7:D4)448,58
C8.49(C7⋊D4) = D14⋊C16central extension (φ=1)224C8.49(C7:D4)448,64
C8.50(C7⋊D4) = C56.9Q8central extension (φ=1)1124C8.50(C7:D4)448,68
C8.51(C7⋊D4) = Dic14.C8central extension (φ=1)2244C8.51(C7:D4)448,72
C8.52(C7⋊D4) = C56.91D4central extension (φ=1)224C8.52(C7:D4)448,106

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