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Extensions 1→N→G→Q→1 with N=C23 and Q=C7⋊D4

Direct product G=N×Q with N=C23 and Q=C7⋊D4
dρLabelID
C23×C7⋊D4224C2^3xC7:D4448,1384

Semidirect products G=N:Q with N=C23 and Q=C7⋊D4
extensionφ:Q→Aut NdρLabelID
C23⋊1(C7⋊D4) = C24⋊D14φ: C7⋊D4/C7 → D4 ⊆ Aut C23564C2^3:1(C7:D4)448,566
C23⋊2(C7⋊D4) = 2+ 1+4⋊2D7φ: C7⋊D4/C7 → D4 ⊆ Aut C23568+C2^3:2(C7:D4)448,778
C23⋊3(C7⋊D4) = C24.21D14φ: C7⋊D4/C14 → C22 ⊆ Aut C23224C2^3:3(C7:D4)448,757
C23⋊4(C7⋊D4) = C24⋊7D14φ: C7⋊D4/C14 → C22 ⊆ Aut C23112C2^3:4(C7:D4)448,1257
C23⋊5(C7⋊D4) = C2×Dic7⋊D4φ: C7⋊D4/Dic7 → C2 ⊆ Aut C23224C2^3:5(C7:D4)448,1255
C23⋊6(C7⋊D4) = C2×C23⋊D14φ: C7⋊D4/D14 → C2 ⊆ Aut C23112C2^3:6(C7:D4)448,1252
C23⋊7(C7⋊D4) = C2×C24⋊D7φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C23112C2^3:7(C7:D4)448,1293

Non-split extensions G=N.Q with N=C23 and Q=C7⋊D4
extensionφ:Q→Aut NdρLabelID
C23.1(C7⋊D4) = C7⋊C2≀C4φ: C7⋊D4/C7 → D4 ⊆ Aut C23568+C2^3.1(C7:D4)448,28
C23.2(C7⋊D4) = (C2×C28).D4φ: C7⋊D4/C7 → D4 ⊆ Aut C231128-C2^3.2(C7:D4)448,29
C23.3(C7⋊D4) = C23.D28φ: C7⋊D4/C7 → D4 ⊆ Aut C231128-C2^3.3(C7:D4)448,30
C23.4(C7⋊D4) = C23.2D28φ: C7⋊D4/C7 → D4 ⊆ Aut C23568+C2^3.4(C7:D4)448,31
C23.5(C7⋊D4) = C24⋊Dic7φ: C7⋊D4/C7 → D4 ⊆ Aut C23564C2^3.5(C7:D4)448,93
C23.6(C7⋊D4) = (C22×C28)⋊C4φ: C7⋊D4/C7 → D4 ⊆ Aut C231124C2^3.6(C7:D4)448,96
C23.7(C7⋊D4) = C42⋊2Dic7φ: C7⋊D4/C7 → D4 ⊆ Aut C231124C2^3.7(C7:D4)448,98
C23.8(C7⋊D4) = C42⋊3Dic7φ: C7⋊D4/C7 → D4 ⊆ Aut C23564C2^3.8(C7:D4)448,102
C23.9(C7⋊D4) = C22⋊C4⋊D14φ: C7⋊D4/C7 → D4 ⊆ Aut C231124C2^3.9(C7:D4)448,587
C23.10(C7⋊D4) = C42⋊5D14φ: C7⋊D4/C7 → D4 ⊆ Aut C231124C2^3.10(C7:D4)448,595
C23.11(C7⋊D4) = D28⋊5D4φ: C7⋊D4/C7 → D4 ⊆ Aut C23564C2^3.11(C7:D4)448,611
C23.12(C7⋊D4) = 2+ 1+4⋊D7φ: C7⋊D4/C7 → D4 ⊆ Aut C23568+C2^3.12(C7:D4)448,775
C23.13(C7⋊D4) = 2+ 1+4.D7φ: C7⋊D4/C7 → D4 ⊆ Aut C231128-C2^3.13(C7:D4)448,776
C23.14(C7⋊D4) = 2+ 1+4.2D7φ: C7⋊D4/C7 → D4 ⊆ Aut C231128-C2^3.14(C7:D4)448,777
C23.15(C7⋊D4) = C24.2D14φ: C7⋊D4/C14 → C22 ⊆ Aut C23112C2^3.15(C7:D4)448,84
C23.16(C7⋊D4) = C42⋊Dic7φ: C7⋊D4/C14 → C22 ⊆ Aut C231124C2^3.16(C7:D4)448,88
C23.17(C7⋊D4) = C24.9D14φ: C7⋊D4/C14 → C22 ⊆ Aut C23224C2^3.17(C7:D4)448,486
C23.18(C7⋊D4) = C24.14D14φ: C7⋊D4/C14 → C22 ⊆ Aut C23224C2^3.18(C7:D4)448,493
C23.19(C7⋊D4) = C4⋊C4.233D14φ: C7⋊D4/C14 → C22 ⊆ Aut C23224C2^3.19(C7:D4)448,530
C23.20(C7⋊D4) = C4⋊C4.236D14φ: C7⋊D4/C14 → C22 ⊆ Aut C23224C2^3.20(C7:D4)448,537
C23.21(C7⋊D4) = C42⋊4D14φ: C7⋊D4/C14 → C22 ⊆ Aut C231124C2^3.21(C7:D4)448,539
C23.22(C7⋊D4) = (C2×D4).D14φ: C7⋊D4/C14 → C22 ⊆ Aut C23224C2^3.22(C7:D4)448,569
C23.23(C7⋊D4) = D28⋊17D4φ: C7⋊D4/C14 → C22 ⊆ Aut C23224C2^3.23(C7:D4)448,571
C23.24(C7⋊D4) = C4⋊D4⋊D7φ: C7⋊D4/C14 → C22 ⊆ Aut C23224C2^3.24(C7:D4)448,573
C23.25(C7⋊D4) = C7⋊C8⋊5D4φ: C7⋊D4/C14 → C22 ⊆ Aut C23224C2^3.25(C7:D4)448,576
C23.26(C7⋊D4) = C14.(C4○D8)φ: C7⋊D4/C14 → C22 ⊆ Aut C23224C2^3.26(C7:D4)448,579
C23.27(C7⋊D4) = D28.37D4φ: C7⋊D4/C14 → C22 ⊆ Aut C23224C2^3.27(C7:D4)448,581
C23.28(C7⋊D4) = C7⋊C8⋊6D4φ: C7⋊D4/C14 → C22 ⊆ Aut C23224C2^3.28(C7:D4)448,583
C23.29(C7⋊D4) = C7⋊C8.6D4φ: C7⋊D4/C14 → C22 ⊆ Aut C23224C2^3.29(C7:D4)448,586
C23.30(C7⋊D4) = C24.20D14φ: C7⋊D4/C14 → C22 ⊆ Aut C23224C2^3.30(C7:D4)448,756
C23.31(C7⋊D4) = (D4×C14)⋊9C4φ: C7⋊D4/C14 → C22 ⊆ Aut C231124C2^3.31(C7:D4)448,770
C23.32(C7⋊D4) = (C7×D4)⋊14D4φ: C7⋊D4/C14 → C22 ⊆ Aut C23224C2^3.32(C7:D4)448,772
C23.33(C7⋊D4) = (C7×D4).32D4φ: C7⋊D4/C14 → C22 ⊆ Aut C23224C2^3.33(C7:D4)448,773
C23.34(C7⋊D4) = C28.C24φ: C7⋊D4/C14 → C22 ⊆ Aut C231124C2^3.34(C7:D4)448,1275
C23.35(C7⋊D4) = C24.44D14φ: C7⋊D4/Dic7 → C2 ⊆ Aut C23224C2^3.35(C7:D4)448,476
C23.36(C7⋊D4) = C23.45D28φ: C7⋊D4/Dic7 → C2 ⊆ Aut C23224C2^3.36(C7:D4)448,492
C23.37(C7⋊D4) = C28.45(C4⋊C4)φ: C7⋊D4/Dic7 → C2 ⊆ Aut C23224C2^3.37(C7:D4)448,532
C23.38(C7⋊D4) = C4.(C2×D28)φ: C7⋊D4/Dic7 → C2 ⊆ Aut C23224C2^3.38(C7:D4)448,536
C23.39(C7⋊D4) = C7⋊C8⋊22D4φ: C7⋊D4/Dic7 → C2 ⊆ Aut C23224C2^3.39(C7:D4)448,572
C23.40(C7⋊D4) = C7⋊C8⋊23D4φ: C7⋊D4/Dic7 → C2 ⊆ Aut C23224C2^3.40(C7:D4)448,575
C23.41(C7⋊D4) = C7⋊C8⋊24D4φ: C7⋊D4/Dic7 → C2 ⊆ Aut C23224C2^3.41(C7:D4)448,582
C23.42(C7⋊D4) = C7⋊C8.29D4φ: C7⋊D4/Dic7 → C2 ⊆ Aut C23224C2^3.42(C7:D4)448,585
C23.43(C7⋊D4) = C24.18D14φ: C7⋊D4/Dic7 → C2 ⊆ Aut C23224C2^3.43(C7:D4)448,754
C23.44(C7⋊D4) = C28.(C2×D4)φ: C7⋊D4/Dic7 → C2 ⊆ Aut C23224C2^3.44(C7:D4)448,767
C23.45(C7⋊D4) = C2×D4.8D14φ: C7⋊D4/Dic7 → C2 ⊆ Aut C23224C2^3.45(C7:D4)448,1274
C23.46(C7⋊D4) = C24.D14φ: C7⋊D4/D14 → C2 ⊆ Aut C23112C2^3.46(C7:D4)448,83
C23.47(C7⋊D4) = C28.2C42φ: C7⋊D4/D14 → C2 ⊆ Aut C23112C2^3.47(C7:D4)448,89
C23.48(C7⋊D4) = (D4×C14)⋊C4φ: C7⋊D4/D14 → C2 ⊆ Aut C23112C2^3.48(C7:D4)448,94
C23.49(C7⋊D4) = C4⋊C4⋊Dic7φ: C7⋊D4/D14 → C2 ⊆ Aut C23112C2^3.49(C7:D4)448,95
C23.50(C7⋊D4) = C23.42D28φ: C7⋊D4/D14 → C2 ⊆ Aut C23224C2^3.50(C7:D4)448,477
C23.51(C7⋊D4) = C24.46D14φ: C7⋊D4/D14 → C2 ⊆ Aut C23224C2^3.51(C7:D4)448,480
C23.52(C7⋊D4) = C23.44D28φ: C7⋊D4/D14 → C2 ⊆ Aut C23112C2^3.52(C7:D4)448,489
C23.53(C7⋊D4) = C28.(C2×Q8)φ: C7⋊D4/D14 → C2 ⊆ Aut C23224C2^3.53(C7:D4)448,529
C23.54(C7⋊D4) = C4⋊C4⋊36D14φ: C7⋊D4/D14 → C2 ⊆ Aut C23112C2^3.54(C7:D4)448,535
C23.55(C7⋊D4) = (C2×C4).47D28φ: C7⋊D4/D14 → C2 ⊆ Aut C23224C2^3.55(C7:D4)448,538
C23.56(C7⋊D4) = (C2×C14).D8φ: C7⋊D4/D14 → C2 ⊆ Aut C23224C2^3.56(C7:D4)448,567
C23.57(C7⋊D4) = C4⋊D4.D7φ: C7⋊D4/D14 → C2 ⊆ Aut C23224C2^3.57(C7:D4)448,568
C23.58(C7⋊D4) = D28⋊16D4φ: C7⋊D4/D14 → C2 ⊆ Aut C23112C2^3.58(C7:D4)448,570
C23.59(C7⋊D4) = Dic14⋊17D4φ: C7⋊D4/D14 → C2 ⊆ Aut C23224C2^3.59(C7:D4)448,574
C23.60(C7⋊D4) = C22⋊Q8.D7φ: C7⋊D4/D14 → C2 ⊆ Aut C23224C2^3.60(C7:D4)448,577
C23.61(C7⋊D4) = (C2×C14).Q16φ: C7⋊D4/D14 → C2 ⊆ Aut C23224C2^3.61(C7:D4)448,578
C23.62(C7⋊D4) = D28.36D4φ: C7⋊D4/D14 → C2 ⊆ Aut C23112C2^3.62(C7:D4)448,580
C23.63(C7⋊D4) = Dic14.37D4φ: C7⋊D4/D14 → C2 ⊆ Aut C23224C2^3.63(C7:D4)448,584
C23.64(C7⋊D4) = C2×C23⋊Dic7φ: C7⋊D4/D14 → C2 ⊆ Aut C23112C2^3.64(C7:D4)448,753
C23.65(C7⋊D4) = C4○D4⋊Dic7φ: C7⋊D4/D14 → C2 ⊆ Aut C23224C2^3.65(C7:D4)448,766
C23.66(C7⋊D4) = C2×D4⋊2Dic7φ: C7⋊D4/D14 → C2 ⊆ Aut C23112C2^3.66(C7:D4)448,769
C23.67(C7⋊D4) = C2×C23.18D14φ: C7⋊D4/D14 → C2 ⊆ Aut C23224C2^3.67(C7:D4)448,1249
C23.68(C7⋊D4) = C2×D4⋊D14φ: C7⋊D4/D14 → C2 ⊆ Aut C23112C2^3.68(C7:D4)448,1273
C23.69(C7⋊D4) = C2×D4.9D14φ: C7⋊D4/D14 → C2 ⊆ Aut C23224C2^3.69(C7:D4)448,1276
C23.70(C7⋊D4) = C14.C4≀C2φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C23112C2^3.70(C7:D4)448,8
C23.71(C7⋊D4) = C4⋊Dic7⋊C4φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C23112C2^3.71(C7:D4)448,9
C23.72(C7⋊D4) = C28.8C42φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C23112C2^3.72(C7:D4)448,80
C23.73(C7⋊D4) = C2×Dic14⋊C4φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C23112C2^3.73(C7:D4)448,461
C23.74(C7⋊D4) = C2×C23.1D14φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C23112C2^3.74(C7:D4)448,488
C23.75(C7⋊D4) = C4.Dic7⋊C4φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C23224C2^3.75(C7:D4)448,498
C23.76(C7⋊D4) = C4○D28⋊C4φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C23224C2^3.76(C7:D4)448,500
C23.77(C7⋊D4) = (C2×C14).40D8φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C23224C2^3.77(C7:D4)448,501
C23.78(C7⋊D4) = C4⋊C4.228D14φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C23224C2^3.78(C7:D4)448,502
C23.79(C7⋊D4) = C4⋊C4.230D14φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C23224C2^3.79(C7:D4)448,504
C23.80(C7⋊D4) = C4⋊C4.231D14φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C23224C2^3.80(C7:D4)448,505
C23.81(C7⋊D4) = C24.62D14φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C23224C2^3.81(C7:D4)448,744
C23.82(C7⋊D4) = C24.63D14φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C23224C2^3.82(C7:D4)448,745
C23.83(C7⋊D4) = C23.28D28φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C23224C2^3.83(C7:D4)448,747
C23.84(C7⋊D4) = (D4×C14)⋊6C4φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C23112C2^3.84(C7:D4)448,749
C23.85(C7⋊D4) = (C2×C14)⋊8D8φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C23112C2^3.85(C7:D4)448,751
C23.86(C7⋊D4) = (C7×D4).31D4φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C23112C2^3.86(C7:D4)448,752
C23.87(C7⋊D4) = (Q8×C14)⋊6C4φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C23224C2^3.87(C7:D4)448,759
C23.88(C7⋊D4) = (C7×Q8)⋊13D4φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C23224C2^3.88(C7:D4)448,761
C23.89(C7⋊D4) = (C2×C14)⋊8Q16φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C23224C2^3.89(C7:D4)448,762
C23.90(C7⋊D4) = C25.D7φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C23112C2^3.90(C7:D4)448,781
C23.91(C7⋊D4) = C2×C23.23D14φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C23224C2^3.91(C7:D4)448,1242
C23.92(C7⋊D4) = C2×D4.D14φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C23112C2^3.92(C7:D4)448,1246
C23.93(C7⋊D4) = C2×C28.C23φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C23224C2^3.93(C7:D4)448,1261
C23.94(C7⋊D4) = C28.C42central extension (φ=1)448C2^3.94(C7:D4)448,86
C23.95(C7⋊D4) = C2×C28.Q8central extension (φ=1)448C2^3.95(C7:D4)448,496
C23.96(C7⋊D4) = C2×C4.Dic14central extension (φ=1)448C2^3.96(C7:D4)448,497
C23.97(C7⋊D4) = C2×C14.D8central extension (φ=1)224C2^3.97(C7:D4)448,499
C23.98(C7⋊D4) = C2×C14.Q16central extension (φ=1)448C2^3.98(C7:D4)448,503
C23.99(C7⋊D4) = C2×C14.C42central extension (φ=1)448C2^3.99(C7:D4)448,742
C23.100(C7⋊D4) = C2×D4⋊Dic7central extension (φ=1)224C2^3.100(C7:D4)448,748
C23.101(C7⋊D4) = C2×Q8⋊Dic7central extension (φ=1)448C2^3.101(C7:D4)448,758
C23.102(C7⋊D4) = C22×Dic7⋊C4central extension (φ=1)448C2^3.102(C7:D4)448,1236
C23.103(C7⋊D4) = C22×D14⋊C4central extension (φ=1)224C2^3.103(C7:D4)448,1240
C23.104(C7⋊D4) = C22×D4⋊D7central extension (φ=1)224C2^3.104(C7:D4)448,1245
C23.105(C7⋊D4) = C22×D4.D7central extension (φ=1)224C2^3.105(C7:D4)448,1247
C23.106(C7⋊D4) = C22×Q8⋊D7central extension (φ=1)224C2^3.106(C7:D4)448,1260
C23.107(C7⋊D4) = C22×C7⋊Q16central extension (φ=1)448C2^3.107(C7:D4)448,1262
C23.108(C7⋊D4) = C22×C23.D7central extension (φ=1)224C2^3.108(C7:D4)448,1292

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