# Extensions 1→N→G→Q→1 with N=C4 and Q=C7×C4○D4

Direct product G=N×Q with N=C4 and Q=C7×C4○D4
dρLabelID
C4○D4×C28224C4oD4xC28448,1300

Semidirect products G=N:Q with N=C4 and Q=C7×C4○D4
extensionφ:Q→Aut NdρLabelID
C41(C7×C4○D4) = C7×C22.26C24φ: C7×C4○D4/C2×C28C2 ⊆ Aut C4224C4:1(C7xC4oD4)448,1315
C42(C7×C4○D4) = C7×D46D4φ: C7×C4○D4/C7×D4C2 ⊆ Aut C4224C4:2(C7xC4oD4)448,1330
C43(C7×C4○D4) = C7×Q86D4φ: C7×C4○D4/C7×Q8C2 ⊆ Aut C4224C4:3(C7xC4oD4)448,1333

Non-split extensions G=N.Q with N=C4 and Q=C7×C4○D4
extensionφ:Q→Aut NdρLabelID
C4.1(C7×C4○D4) = D8×C28φ: C7×C4○D4/C2×C28C2 ⊆ Aut C4224C4.1(C7xC4oD4)448,845
C4.2(C7×C4○D4) = SD16×C28φ: C7×C4○D4/C2×C28C2 ⊆ Aut C4224C4.2(C7xC4oD4)448,846
C4.3(C7×C4○D4) = Q16×C28φ: C7×C4○D4/C2×C28C2 ⊆ Aut C4448C4.3(C7xC4oD4)448,847
C4.4(C7×C4○D4) = C7×SD16⋊C4φ: C7×C4○D4/C2×C28C2 ⊆ Aut C4224C4.4(C7xC4oD4)448,848
C4.5(C7×C4○D4) = C7×Q16⋊C4φ: C7×C4○D4/C2×C28C2 ⊆ Aut C4448C4.5(C7xC4oD4)448,849
C4.6(C7×C4○D4) = C7×D8⋊C4φ: C7×C4○D4/C2×C28C2 ⊆ Aut C4224C4.6(C7xC4oD4)448,850
C4.7(C7×C4○D4) = C7×C88D4φ: C7×C4○D4/C2×C28C2 ⊆ Aut C4224C4.7(C7xC4oD4)448,873
C4.8(C7×C4○D4) = C7×C87D4φ: C7×C4○D4/C2×C28C2 ⊆ Aut C4224C4.8(C7xC4oD4)448,874
C4.9(C7×C4○D4) = C7×C8.18D4φ: C7×C4○D4/C2×C28C2 ⊆ Aut C4224C4.9(C7xC4oD4)448,875
C4.10(C7×C4○D4) = C7×C8⋊D4φ: C7×C4○D4/C2×C28C2 ⊆ Aut C4224C4.10(C7xC4oD4)448,876
C4.11(C7×C4○D4) = C7×C82D4φ: C7×C4○D4/C2×C28C2 ⊆ Aut C4224C4.11(C7xC4oD4)448,877
C4.12(C7×C4○D4) = C7×C8.D4φ: C7×C4○D4/C2×C28C2 ⊆ Aut C4224C4.12(C7xC4oD4)448,878
C4.13(C7×C4○D4) = C7×C4.4D8φ: C7×C4○D4/C2×C28C2 ⊆ Aut C4224C4.13(C7xC4oD4)448,894
C4.14(C7×C4○D4) = C7×C4.SD16φ: C7×C4○D4/C2×C28C2 ⊆ Aut C4448C4.14(C7xC4oD4)448,895
C4.15(C7×C4○D4) = C7×C42.78C22φ: C7×C4○D4/C2×C28C2 ⊆ Aut C4224C4.15(C7xC4oD4)448,896
C4.16(C7×C4○D4) = C7×C42.28C22φ: C7×C4○D4/C2×C28C2 ⊆ Aut C4224C4.16(C7xC4oD4)448,897
C4.17(C7×C4○D4) = C7×C42.29C22φ: C7×C4○D4/C2×C28C2 ⊆ Aut C4224C4.17(C7xC4oD4)448,898
C4.18(C7×C4○D4) = C7×C42.30C22φ: C7×C4○D4/C2×C28C2 ⊆ Aut C4448C4.18(C7xC4oD4)448,899
C4.19(C7×C4○D4) = C7×C23.37C23φ: C7×C4○D4/C2×C28C2 ⊆ Aut C4224C4.19(C7xC4oD4)448,1316
C4.20(C7×C4○D4) = C7×C22.34C24φ: C7×C4○D4/C2×C28C2 ⊆ Aut C4224C4.20(C7xC4oD4)448,1323
C4.21(C7×C4○D4) = C7×C22.35C24φ: C7×C4○D4/C2×C28C2 ⊆ Aut C4224C4.21(C7xC4oD4)448,1324
C4.22(C7×C4○D4) = C7×C22.36C24φ: C7×C4○D4/C2×C28C2 ⊆ Aut C4224C4.22(C7xC4oD4)448,1325
C4.23(C7×C4○D4) = C7×D4⋊Q8φ: C7×C4○D4/C7×D4C2 ⊆ Aut C4224C4.23(C7xC4oD4)448,882
C4.24(C7×C4○D4) = C7×Q8⋊Q8φ: C7×C4○D4/C7×D4C2 ⊆ Aut C4448C4.24(C7xC4oD4)448,883
C4.25(C7×C4○D4) = C7×D42Q8φ: C7×C4○D4/C7×D4C2 ⊆ Aut C4224C4.25(C7xC4oD4)448,884
C4.26(C7×C4○D4) = C7×C4.Q16φ: C7×C4○D4/C7×D4C2 ⊆ Aut C4448C4.26(C7xC4oD4)448,885
C4.27(C7×C4○D4) = C7×D4.Q8φ: C7×C4○D4/C7×D4C2 ⊆ Aut C4224C4.27(C7xC4oD4)448,886
C4.28(C7×C4○D4) = C7×Q8.Q8φ: C7×C4○D4/C7×D4C2 ⊆ Aut C4448C4.28(C7xC4oD4)448,887
C4.29(C7×C4○D4) = C7×C22.D8φ: C7×C4○D4/C7×D4C2 ⊆ Aut C4224C4.29(C7xC4oD4)448,888
C4.30(C7×C4○D4) = C7×C23.46D4φ: C7×C4○D4/C7×D4C2 ⊆ Aut C4224C4.30(C7xC4oD4)448,889
C4.31(C7×C4○D4) = C7×C23.19D4φ: C7×C4○D4/C7×D4C2 ⊆ Aut C4224C4.31(C7xC4oD4)448,890
C4.32(C7×C4○D4) = C7×C23.47D4φ: C7×C4○D4/C7×D4C2 ⊆ Aut C4224C4.32(C7xC4oD4)448,891
C4.33(C7×C4○D4) = C7×C23.48D4φ: C7×C4○D4/C7×D4C2 ⊆ Aut C4224C4.33(C7xC4oD4)448,892
C4.34(C7×C4○D4) = C7×C23.20D4φ: C7×C4○D4/C7×D4C2 ⊆ Aut C4224C4.34(C7xC4oD4)448,893
C4.35(C7×C4○D4) = C7×C22.46C24φ: C7×C4○D4/C7×D4C2 ⊆ Aut C4224C4.35(C7xC4oD4)448,1335
C4.36(C7×C4○D4) = C7×C22.47C24φ: C7×C4○D4/C7×D4C2 ⊆ Aut C4224C4.36(C7xC4oD4)448,1336
C4.37(C7×C4○D4) = C7×D43Q8φ: C7×C4○D4/C7×D4C2 ⊆ Aut C4224C4.37(C7xC4oD4)448,1337
C4.38(C7×C4○D4) = C7×C22.49C24φ: C7×C4○D4/C7×D4C2 ⊆ Aut C4224C4.38(C7xC4oD4)448,1338
C4.39(C7×C4○D4) = C7×C22.50C24φ: C7×C4○D4/C7×D4C2 ⊆ Aut C4224C4.39(C7xC4oD4)448,1339
C4.40(C7×C4○D4) = C7×C4⋊D8φ: C7×C4○D4/C7×Q8C2 ⊆ Aut C4224C4.40(C7xC4oD4)448,867
C4.41(C7×C4○D4) = C7×C4⋊SD16φ: C7×C4○D4/C7×Q8C2 ⊆ Aut C4224C4.41(C7xC4oD4)448,868
C4.42(C7×C4○D4) = C7×D4.D4φ: C7×C4○D4/C7×Q8C2 ⊆ Aut C4224C4.42(C7xC4oD4)448,869
C4.43(C7×C4○D4) = C7×C42Q16φ: C7×C4○D4/C7×Q8C2 ⊆ Aut C4448C4.43(C7xC4oD4)448,870
C4.44(C7×C4○D4) = C7×D4.2D4φ: C7×C4○D4/C7×Q8C2 ⊆ Aut C4224C4.44(C7xC4oD4)448,871
C4.45(C7×C4○D4) = C7×Q8.D4φ: C7×C4○D4/C7×Q8C2 ⊆ Aut C4224C4.45(C7xC4oD4)448,872
C4.46(C7×C4○D4) = C7×Q83Q8φ: C7×C4○D4/C7×Q8C2 ⊆ Aut C4448C4.46(C7xC4oD4)448,1340
C4.47(C7×C4○D4) = C7×C22.53C24φ: C7×C4○D4/C7×Q8C2 ⊆ Aut C4224C4.47(C7xC4oD4)448,1342
C4.48(C7×C4○D4) = C7×C42.12C4central extension (φ=1)224C4.48(C7xC4oD4)448,839
C4.49(C7×C4○D4) = C7×C42.6C4central extension (φ=1)224C4.49(C7xC4oD4)448,840
C4.50(C7×C4○D4) = C7×C42.7C22central extension (φ=1)224C4.50(C7xC4oD4)448,841
C4.51(C7×C4○D4) = D4×C56central extension (φ=1)224C4.51(C7xC4oD4)448,842
C4.52(C7×C4○D4) = C7×C89D4central extension (φ=1)224C4.52(C7xC4oD4)448,843
C4.53(C7×C4○D4) = C7×C86D4central extension (φ=1)224C4.53(C7xC4oD4)448,844
C4.54(C7×C4○D4) = Q8×C56central extension (φ=1)448C4.54(C7xC4oD4)448,853
C4.55(C7×C4○D4) = C7×C84Q8central extension (φ=1)448C4.55(C7xC4oD4)448,854
C4.56(C7×C4○D4) = C7×C23.36C23central extension (φ=1)224C4.56(C7xC4oD4)448,1312

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