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Extensions 1→N→G→Q→1 with N=C4 and Q=C3×C4○D4

Direct product G=N×Q with N=C4 and Q=C3×C4○D4
dρLabelID
C12×C4○D496C12xC4oD4192,1406

Semidirect products G=N:Q with N=C4 and Q=C3×C4○D4
extensionφ:Q→Aut NdρLabelID
C4⋊1(C3×C4○D4) = C3×C22.26C24φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C496C4:1(C3xC4oD4)192,1421
C4⋊2(C3×C4○D4) = C3×D4⋊6D4φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C496C4:2(C3xC4oD4)192,1436
C4⋊3(C3×C4○D4) = C3×Q8⋊6D4φ: C3×C4○D4/C3×Q8 → C2 ⊆ Aut C496C4:3(C3xC4oD4)192,1439

Non-split extensions G=N.Q with N=C4 and Q=C3×C4○D4
extensionφ:Q→Aut NdρLabelID
C4.1(C3×C4○D4) = C12×D8φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C496C4.1(C3xC4oD4)192,870
C4.2(C3×C4○D4) = C12×SD16φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C496C4.2(C3xC4oD4)192,871
C4.3(C3×C4○D4) = C12×Q16φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C4192C4.3(C3xC4oD4)192,872
C4.4(C3×C4○D4) = C3×SD16⋊C4φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C496C4.4(C3xC4oD4)192,873
C4.5(C3×C4○D4) = C3×Q16⋊C4φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C4192C4.5(C3xC4oD4)192,874
C4.6(C3×C4○D4) = C3×D8⋊C4φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C496C4.6(C3xC4oD4)192,875
C4.7(C3×C4○D4) = C3×C8⋊8D4φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C496C4.7(C3xC4oD4)192,898
C4.8(C3×C4○D4) = C3×C8⋊7D4φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C496C4.8(C3xC4oD4)192,899
C4.9(C3×C4○D4) = C3×C8.18D4φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C496C4.9(C3xC4oD4)192,900
C4.10(C3×C4○D4) = C3×C8⋊D4φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C496C4.10(C3xC4oD4)192,901
C4.11(C3×C4○D4) = C3×C8⋊2D4φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C496C4.11(C3xC4oD4)192,902
C4.12(C3×C4○D4) = C3×C8.D4φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C496C4.12(C3xC4oD4)192,903
C4.13(C3×C4○D4) = C3×C4.4D8φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C496C4.13(C3xC4oD4)192,919
C4.14(C3×C4○D4) = C3×C4.SD16φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C4192C4.14(C3xC4oD4)192,920
C4.15(C3×C4○D4) = C3×C42.78C22φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C496C4.15(C3xC4oD4)192,921
C4.16(C3×C4○D4) = C3×C42.28C22φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C496C4.16(C3xC4oD4)192,922
C4.17(C3×C4○D4) = C3×C42.29C22φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C496C4.17(C3xC4oD4)192,923
C4.18(C3×C4○D4) = C3×C42.30C22φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C4192C4.18(C3xC4oD4)192,924
C4.19(C3×C4○D4) = C3×C23.37C23φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C496C4.19(C3xC4oD4)192,1422
C4.20(C3×C4○D4) = C3×C22.34C24φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C496C4.20(C3xC4oD4)192,1429
C4.21(C3×C4○D4) = C3×C22.35C24φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C496C4.21(C3xC4oD4)192,1430
C4.22(C3×C4○D4) = C3×C22.36C24φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C496C4.22(C3xC4oD4)192,1431
C4.23(C3×C4○D4) = C3×D4⋊Q8φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C496C4.23(C3xC4oD4)192,907
C4.24(C3×C4○D4) = C3×Q8⋊Q8φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C4192C4.24(C3xC4oD4)192,908
C4.25(C3×C4○D4) = C3×D4⋊2Q8φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C496C4.25(C3xC4oD4)192,909
C4.26(C3×C4○D4) = C3×C4.Q16φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C4192C4.26(C3xC4oD4)192,910
C4.27(C3×C4○D4) = C3×D4.Q8φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C496C4.27(C3xC4oD4)192,911
C4.28(C3×C4○D4) = C3×Q8.Q8φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C4192C4.28(C3xC4oD4)192,912
C4.29(C3×C4○D4) = C3×C22.D8φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C496C4.29(C3xC4oD4)192,913
C4.30(C3×C4○D4) = C3×C23.46D4φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C496C4.30(C3xC4oD4)192,914
C4.31(C3×C4○D4) = C3×C23.19D4φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C496C4.31(C3xC4oD4)192,915
C4.32(C3×C4○D4) = C3×C23.47D4φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C496C4.32(C3xC4oD4)192,916
C4.33(C3×C4○D4) = C3×C23.48D4φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C496C4.33(C3xC4oD4)192,917
C4.34(C3×C4○D4) = C3×C23.20D4φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C496C4.34(C3xC4oD4)192,918
C4.35(C3×C4○D4) = C3×C22.46C24φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C496C4.35(C3xC4oD4)192,1441
C4.36(C3×C4○D4) = C3×C22.47C24φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C496C4.36(C3xC4oD4)192,1442
C4.37(C3×C4○D4) = C3×D4⋊3Q8φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C496C4.37(C3xC4oD4)192,1443
C4.38(C3×C4○D4) = C3×C22.49C24φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C496C4.38(C3xC4oD4)192,1444
C4.39(C3×C4○D4) = C3×C22.50C24φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C496C4.39(C3xC4oD4)192,1445
C4.40(C3×C4○D4) = C3×C4⋊D8φ: C3×C4○D4/C3×Q8 → C2 ⊆ Aut C496C4.40(C3xC4oD4)192,892
C4.41(C3×C4○D4) = C3×C4⋊SD16φ: C3×C4○D4/C3×Q8 → C2 ⊆ Aut C496C4.41(C3xC4oD4)192,893
C4.42(C3×C4○D4) = C3×D4.D4φ: C3×C4○D4/C3×Q8 → C2 ⊆ Aut C496C4.42(C3xC4oD4)192,894
C4.43(C3×C4○D4) = C3×C4⋊2Q16φ: C3×C4○D4/C3×Q8 → C2 ⊆ Aut C4192C4.43(C3xC4oD4)192,895
C4.44(C3×C4○D4) = C3×D4.2D4φ: C3×C4○D4/C3×Q8 → C2 ⊆ Aut C496C4.44(C3xC4oD4)192,896
C4.45(C3×C4○D4) = C3×Q8.D4φ: C3×C4○D4/C3×Q8 → C2 ⊆ Aut C496C4.45(C3xC4oD4)192,897
C4.46(C3×C4○D4) = C3×Q8⋊3Q8φ: C3×C4○D4/C3×Q8 → C2 ⊆ Aut C4192C4.46(C3xC4oD4)192,1446
C4.47(C3×C4○D4) = C3×C22.53C24φ: C3×C4○D4/C3×Q8 → C2 ⊆ Aut C496C4.47(C3xC4oD4)192,1448
C4.48(C3×C4○D4) = C3×C42.12C4central extension (φ=1)96C4.48(C3xC4oD4)192,864
C4.49(C3×C4○D4) = C3×C42.6C4central extension (φ=1)96C4.49(C3xC4oD4)192,865
C4.50(C3×C4○D4) = C3×C42.7C22central extension (φ=1)96C4.50(C3xC4oD4)192,866
C4.51(C3×C4○D4) = D4×C24central extension (φ=1)96C4.51(C3xC4oD4)192,867
C4.52(C3×C4○D4) = C3×C8⋊9D4central extension (φ=1)96C4.52(C3xC4oD4)192,868
C4.53(C3×C4○D4) = C3×C8⋊6D4central extension (φ=1)96C4.53(C3xC4oD4)192,869
C4.54(C3×C4○D4) = Q8×C24central extension (φ=1)192C4.54(C3xC4oD4)192,878
C4.55(C3×C4○D4) = C3×C8⋊4Q8central extension (φ=1)192C4.55(C3xC4oD4)192,879
C4.56(C3×C4○D4) = C3×C23.36C23central extension (φ=1)96C4.56(C3xC4oD4)192,1418

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