# Extensions 1→N→G→Q→1 with N=C14 and Q=C4×D4

Direct product G=N×Q with N=C14 and Q=C4×D4
dρLabelID
D4×C2×C28224D4xC2xC28448,1298

Semidirect products G=N:Q with N=C14 and Q=C4×D4
extensionφ:Q→Aut NdρLabelID
C141(C4×D4) = C2×C4×D28φ: C4×D4/C42C2 ⊆ Aut C14224C14:1(C4xD4)448,926
C142(C4×D4) = C2×Dic74D4φ: C4×D4/C22⋊C4C2 ⊆ Aut C14224C14:2(C4xD4)448,938
C143(C4×D4) = C2×D28⋊C4φ: C4×D4/C4⋊C4C2 ⊆ Aut C14224C14:3(C4xD4)448,956
C144(C4×D4) = C2×C4×C7⋊D4φ: C4×D4/C22×C4C2 ⊆ Aut C14224C14:4(C4xD4)448,1241
C145(C4×D4) = C2×D4×Dic7φ: C4×D4/C2×D4C2 ⊆ Aut C14224C14:5(C4xD4)448,1248

Non-split extensions G=N.Q with N=C14 and Q=C4×D4
extensionφ:Q→Aut NdρLabelID
C14.1(C4×D4) = C4⋊Dic77C4φ: C4×D4/C42C2 ⊆ Aut C14448C14.1(C4xD4)448,187
C14.2(C4×D4) = (C2×C4)⋊9D28φ: C4×D4/C42C2 ⊆ Aut C14224C14.2(C4xD4)448,199
C14.3(C4×D4) = D14⋊C4⋊C4φ: C4×D4/C42C2 ⊆ Aut C14224C14.3(C4xD4)448,202
C14.4(C4×D4) = C8×D28φ: C4×D4/C42C2 ⊆ Aut C14224C14.4(C4xD4)448,220
C14.5(C4×D4) = C86D28φ: C4×D4/C42C2 ⊆ Aut C14224C14.5(C4xD4)448,222
C14.6(C4×D4) = C4×C56⋊C2φ: C4×D4/C42C2 ⊆ Aut C14224C14.6(C4xD4)448,225
C14.7(C4×D4) = C4×D56φ: C4×D4/C42C2 ⊆ Aut C14224C14.7(C4xD4)448,226
C14.8(C4×D4) = C4×Dic28φ: C4×D4/C42C2 ⊆ Aut C14448C14.8(C4xD4)448,232
C14.9(C4×D4) = D5611C4φ: C4×D4/C42C2 ⊆ Aut C141122C14.9(C4xD4)448,234
C14.10(C4×D4) = C89D28φ: C4×D4/C42C2 ⊆ Aut C14224C14.10(C4xD4)448,240
C14.11(C4×D4) = C42.16D14φ: C4×D4/C42C2 ⊆ Aut C14224C14.11(C4xD4)448,244
C14.12(C4×D4) = D56⋊C4φ: C4×D4/C42C2 ⊆ Aut C14224C14.12(C4xD4)448,245
C14.13(C4×D4) = Dic28⋊C4φ: C4×D4/C42C2 ⊆ Aut C14448C14.13(C4xD4)448,250
C14.14(C4×D4) = D564C4φ: C4×D4/C42C2 ⊆ Aut C141124C14.14(C4xD4)448,251
C14.15(C4×D4) = C284(C4⋊C4)φ: C4×D4/C42C2 ⊆ Aut C14448C14.15(C4xD4)448,462
C14.16(C4×D4) = C4×C4⋊Dic7φ: C4×D4/C42C2 ⊆ Aut C14448C14.16(C4xD4)448,468
C14.17(C4×D4) = C4×D14⋊C4φ: C4×D4/C42C2 ⊆ Aut C14224C14.17(C4xD4)448,472
C14.18(C4×D4) = (C2×C4)⋊6D28φ: C4×D4/C42C2 ⊆ Aut C14224C14.18(C4xD4)448,473
C14.19(C4×D4) = C14.(C4×Q8)φ: C4×D4/C22⋊C4C2 ⊆ Aut C14448C14.19(C4xD4)448,181
C14.20(C4×D4) = Dic7⋊C42φ: C4×D4/C22⋊C4C2 ⊆ Aut C14448C14.20(C4xD4)448,183
C14.21(C4×D4) = Dic7⋊C4⋊C4φ: C4×D4/C22⋊C4C2 ⊆ Aut C14448C14.21(C4xD4)448,186
C14.22(C4×D4) = C14.(C4×D4)φ: C4×D4/C22⋊C4C2 ⊆ Aut C14448C14.22(C4xD4)448,189
C14.23(C4×D4) = D14⋊C42φ: C4×D4/C22⋊C4C2 ⊆ Aut C14224C14.23(C4xD4)448,200
C14.24(C4×D4) = D14⋊C45C4φ: C4×D4/C22⋊C4C2 ⊆ Aut C14224C14.24(C4xD4)448,203
C14.25(C4×D4) = C2.(C4×D28)φ: C4×D4/C22⋊C4C2 ⊆ Aut C14224C14.25(C4xD4)448,204
C14.26(C4×D4) = C7⋊D4⋊C8φ: C4×D4/C22⋊C4C2 ⊆ Aut C14224C14.26(C4xD4)448,259
C14.27(C4×D4) = D142M4(2)φ: C4×D4/C22⋊C4C2 ⊆ Aut C14224C14.27(C4xD4)448,262
C14.28(C4×D4) = Dic7⋊M4(2)φ: C4×D4/C22⋊C4C2 ⊆ Aut C14224C14.28(C4xD4)448,263
C14.29(C4×D4) = C7⋊C826D4φ: C4×D4/C22⋊C4C2 ⊆ Aut C14224C14.29(C4xD4)448,264
C14.30(C4×D4) = Dic74D8φ: C4×D4/C22⋊C4C2 ⊆ Aut C14224C14.30(C4xD4)448,290
C14.31(C4×D4) = D4.D7⋊C4φ: C4×D4/C22⋊C4C2 ⊆ Aut C14224C14.31(C4xD4)448,291
C14.32(C4×D4) = Dic76SD16φ: C4×D4/C22⋊C4C2 ⊆ Aut C14224C14.32(C4xD4)448,292
C14.33(C4×D4) = D4⋊D7⋊C4φ: C4×D4/C22⋊C4C2 ⊆ Aut C14224C14.33(C4xD4)448,319
C14.34(C4×D4) = Dic77SD16φ: C4×D4/C22⋊C4C2 ⊆ Aut C14224C14.34(C4xD4)448,322
C14.35(C4×D4) = C7⋊Q16⋊C4φ: C4×D4/C22⋊C4C2 ⊆ Aut C14448C14.35(C4xD4)448,323
C14.36(C4×D4) = Dic74Q16φ: C4×D4/C22⋊C4C2 ⊆ Aut C14448C14.36(C4xD4)448,324
C14.37(C4×D4) = Q8⋊D7⋊C4φ: C4×D4/C22⋊C4C2 ⊆ Aut C14224C14.37(C4xD4)448,351
C14.38(C4×D4) = M4(2).22D14φ: C4×D4/C22⋊C4C2 ⊆ Aut C141124C14.38(C4xD4)448,357
C14.39(C4×D4) = C42.196D14φ: C4×D4/C22⋊C4C2 ⊆ Aut C141124C14.39(C4xD4)448,358
C14.40(C4×D4) = C22⋊C4×Dic7φ: C4×D4/C22⋊C4C2 ⊆ Aut C14224C14.40(C4xD4)448,475
C14.41(C4×D4) = C24.3D14φ: C4×D4/C22⋊C4C2 ⊆ Aut C14224C14.41(C4xD4)448,478
C14.42(C4×D4) = C24.4D14φ: C4×D4/C22⋊C4C2 ⊆ Aut C14224C14.42(C4xD4)448,479
C14.43(C4×D4) = C24.46D14φ: C4×D4/C22⋊C4C2 ⊆ Aut C14224C14.43(C4xD4)448,480
C14.44(C4×D4) = C23.45D28φ: C4×D4/C22⋊C4C2 ⊆ Aut C14224C14.44(C4xD4)448,492
C14.45(C4×D4) = C4⋊Dic78C4φ: C4×D4/C4⋊C4C2 ⊆ Aut C14448C14.45(C4xD4)448,188
C14.46(C4×D4) = D28⋊C8φ: C4×D4/C4⋊C4C2 ⊆ Aut C14224C14.46(C4xD4)448,368
C14.47(C4×D4) = D143M4(2)φ: C4×D4/C4⋊C4C2 ⊆ Aut C14224C14.47(C4xD4)448,370
C14.48(C4×D4) = C282M4(2)φ: C4×D4/C4⋊C4C2 ⊆ Aut C14224C14.48(C4xD4)448,372
C14.49(C4×D4) = Dic78SD16φ: C4×D4/C4⋊C4C2 ⊆ Aut C14224C14.49(C4xD4)448,386
C14.50(C4×D4) = Dic289C4φ: C4×D4/C4⋊C4C2 ⊆ Aut C14448C14.50(C4xD4)448,387
C14.51(C4×D4) = D569C4φ: C4×D4/C4⋊C4C2 ⊆ Aut C14224C14.51(C4xD4)448,403
C14.52(C4×D4) = Dic75D8φ: C4×D4/C4⋊C4C2 ⊆ Aut C14224C14.52(C4xD4)448,406
C14.53(C4×D4) = Dic286C4φ: C4×D4/C4⋊C4C2 ⊆ Aut C14448C14.53(C4xD4)448,407
C14.54(C4×D4) = C56⋊C2⋊C4φ: C4×D4/C4⋊C4C2 ⊆ Aut C14224C14.54(C4xD4)448,423
C14.55(C4×D4) = D5610C4φ: C4×D4/C4⋊C4C2 ⊆ Aut C141124C14.55(C4xD4)448,428
C14.56(C4×D4) = D567C4φ: C4×D4/C4⋊C4C2 ⊆ Aut C141124C14.56(C4xD4)448,429
C14.57(C4×D4) = C28⋊(C4⋊C4)φ: C4×D4/C4⋊C4C2 ⊆ Aut C14448C14.57(C4xD4)448,507
C14.58(C4×D4) = C4⋊C4×Dic7φ: C4×D4/C4⋊C4C2 ⊆ Aut C14448C14.58(C4xD4)448,509
C14.59(C4×D4) = (C2×D28)⋊10C4φ: C4×D4/C4⋊C4C2 ⊆ Aut C14224C14.59(C4xD4)448,522
C14.60(C4×D4) = D14⋊C47C4φ: C4×D4/C4⋊C4C2 ⊆ Aut C14224C14.60(C4xD4)448,524
C14.61(C4×D4) = C4×Dic7⋊C4φ: C4×D4/C22×C4C2 ⊆ Aut C14448C14.61(C4xD4)448,465
C14.62(C4×D4) = (C2×C42).D7φ: C4×D4/C22×C4C2 ⊆ Aut C14448C14.62(C4xD4)448,467
C14.63(C4×D4) = (C2×C42)⋊D7φ: C4×D4/C22×C4C2 ⊆ Aut C14224C14.63(C4xD4)448,474
C14.64(C4×D4) = C24.12D14φ: C4×D4/C22×C4C2 ⊆ Aut C14224C14.64(C4xD4)448,490
C14.65(C4×D4) = C24.13D14φ: C4×D4/C22×C4C2 ⊆ Aut C14224C14.65(C4xD4)448,491
C14.66(C4×D4) = Dic7⋊(C4⋊C4)φ: C4×D4/C22×C4C2 ⊆ Aut C14448C14.66(C4xD4)448,506
C14.67(C4×D4) = C22.23(Q8×D7)φ: C4×D4/C22×C4C2 ⊆ Aut C14448C14.67(C4xD4)448,512
C14.68(C4×D4) = D14⋊C46C4φ: C4×D4/C22×C4C2 ⊆ Aut C14224C14.68(C4xD4)448,523
C14.69(C4×D4) = C4×D4⋊D7φ: C4×D4/C22×C4C2 ⊆ Aut C14224C14.69(C4xD4)448,547
C14.70(C4×D4) = C42.48D14φ: C4×D4/C22×C4C2 ⊆ Aut C14224C14.70(C4xD4)448,548
C14.71(C4×D4) = C4×D4.D7φ: C4×D4/C22×C4C2 ⊆ Aut C14224C14.71(C4xD4)448,551
C14.72(C4×D4) = C42.51D14φ: C4×D4/C22×C4C2 ⊆ Aut C14224C14.72(C4xD4)448,552
C14.73(C4×D4) = C4×Q8⋊D7φ: C4×D4/C22×C4C2 ⊆ Aut C14224C14.73(C4xD4)448,559
C14.74(C4×D4) = C42.56D14φ: C4×D4/C22×C4C2 ⊆ Aut C14224C14.74(C4xD4)448,560
C14.75(C4×D4) = C4×C7⋊Q16φ: C4×D4/C22×C4C2 ⊆ Aut C14448C14.75(C4xD4)448,563
C14.76(C4×D4) = C42.59D14φ: C4×D4/C22×C4C2 ⊆ Aut C14448C14.76(C4xD4)448,564
C14.77(C4×D4) = C8×C7⋊D4φ: C4×D4/C22×C4C2 ⊆ Aut C14224C14.77(C4xD4)448,643
C14.78(C4×D4) = C5632D4φ: C4×D4/C22×C4C2 ⊆ Aut C14224C14.78(C4xD4)448,645
C14.79(C4×D4) = C56⋊D4φ: C4×D4/C22×C4C2 ⊆ Aut C14224C14.79(C4xD4)448,661
C14.80(C4×D4) = C5618D4φ: C4×D4/C22×C4C2 ⊆ Aut C14224C14.80(C4xD4)448,662
C14.81(C4×D4) = C56.93D4φ: C4×D4/C22×C4C2 ⊆ Aut C141124C14.81(C4xD4)448,678
C14.82(C4×D4) = C56.50D4φ: C4×D4/C22×C4C2 ⊆ Aut C141124C14.82(C4xD4)448,679
C14.83(C4×D4) = C4×C23.D7φ: C4×D4/C22×C4C2 ⊆ Aut C14224C14.83(C4xD4)448,743
C14.84(C4×D4) = C24.62D14φ: C4×D4/C22×C4C2 ⊆ Aut C14224C14.84(C4xD4)448,744
C14.85(C4×D4) = C23.28D28φ: C4×D4/C22×C4C2 ⊆ Aut C14224C14.85(C4xD4)448,747
C14.86(C4×D4) = C24.47D14φ: C4×D4/C2×D4C2 ⊆ Aut C14224C14.86(C4xD4)448,484
C14.87(C4×D4) = C24.8D14φ: C4×D4/C2×D4C2 ⊆ Aut C14224C14.87(C4xD4)448,485
C14.88(C4×D4) = C4⋊C45Dic7φ: C4×D4/C2×D4C2 ⊆ Aut C14448C14.88(C4xD4)448,515
C14.89(C4×D4) = C4⋊(C4⋊Dic7)φ: C4×D4/C2×D4C2 ⊆ Aut C14448C14.89(C4xD4)448,519
C14.90(C4×D4) = D4×C7⋊C8φ: C4×D4/C2×D4C2 ⊆ Aut C14224C14.90(C4xD4)448,544
C14.91(C4×D4) = C42.47D14φ: C4×D4/C2×D4C2 ⊆ Aut C14224C14.91(C4xD4)448,545
C14.92(C4×D4) = C283M4(2)φ: C4×D4/C2×D4C2 ⊆ Aut C14224C14.92(C4xD4)448,546
C14.93(C4×D4) = D8×Dic7φ: C4×D4/C2×D4C2 ⊆ Aut C14224C14.93(C4xD4)448,683
C14.94(C4×D4) = D8⋊Dic7φ: C4×D4/C2×D4C2 ⊆ Aut C14224C14.94(C4xD4)448,686
C14.95(C4×D4) = SD16×Dic7φ: C4×D4/C2×D4C2 ⊆ Aut C14224C14.95(C4xD4)448,695
C14.96(C4×D4) = SD16⋊Dic7φ: C4×D4/C2×D4C2 ⊆ Aut C14224C14.96(C4xD4)448,698
C14.97(C4×D4) = Q16×Dic7φ: C4×D4/C2×D4C2 ⊆ Aut C14448C14.97(C4xD4)448,717
C14.98(C4×D4) = Q16⋊Dic7φ: C4×D4/C2×D4C2 ⊆ Aut C14448C14.98(C4xD4)448,718
C14.99(C4×D4) = D85Dic7φ: C4×D4/C2×D4C2 ⊆ Aut C141124C14.99(C4xD4)448,730
C14.100(C4×D4) = D84Dic7φ: C4×D4/C2×D4C2 ⊆ Aut C141124C14.100(C4xD4)448,731
C14.101(C4×D4) = C24.18D14φ: C4×D4/C2×D4C2 ⊆ Aut C14224C14.101(C4xD4)448,754
C14.102(C4×D4) = C24.19D14φ: C4×D4/C2×D4C2 ⊆ Aut C14224C14.102(C4xD4)448,755
C14.103(C4×D4) = C22⋊C4×C28central extension (φ=1)224C14.103(C4xD4)448,785
C14.104(C4×D4) = C4⋊C4×C28central extension (φ=1)448C14.104(C4xD4)448,786
C14.105(C4×D4) = C7×C23.8Q8central extension (φ=1)224C14.105(C4xD4)448,793
C14.106(C4×D4) = C7×C23.23D4central extension (φ=1)224C14.106(C4xD4)448,794
C14.107(C4×D4) = C7×C23.63C23central extension (φ=1)448C14.107(C4xD4)448,795
C14.108(C4×D4) = C7×C24.C22central extension (φ=1)224C14.108(C4xD4)448,796
C14.109(C4×D4) = C7×C23.65C23central extension (φ=1)448C14.109(C4xD4)448,797
C14.110(C4×D4) = C7×C24.3C22central extension (φ=1)224C14.110(C4xD4)448,798
C14.111(C4×D4) = D4×C56central extension (φ=1)224C14.111(C4xD4)448,842
C14.112(C4×D4) = C7×C89D4central extension (φ=1)224C14.112(C4xD4)448,843
C14.113(C4×D4) = C7×C86D4central extension (φ=1)224C14.113(C4xD4)448,844
C14.114(C4×D4) = D8×C28central extension (φ=1)224C14.114(C4xD4)448,845
C14.115(C4×D4) = SD16×C28central extension (φ=1)224C14.115(C4xD4)448,846
C14.116(C4×D4) = Q16×C28central extension (φ=1)448C14.116(C4xD4)448,847
C14.117(C4×D4) = C7×SD16⋊C4central extension (φ=1)224C14.117(C4xD4)448,848
C14.118(C4×D4) = C7×Q16⋊C4central extension (φ=1)448C14.118(C4xD4)448,849
C14.119(C4×D4) = C7×D8⋊C4central extension (φ=1)224C14.119(C4xD4)448,850
C14.120(C4×D4) = C7×C8○D8central extension (φ=1)1122C14.120(C4xD4)448,851
C14.121(C4×D4) = C7×C8.26D4central extension (φ=1)1124C14.121(C4xD4)448,852

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