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Extensions 1→N→G→Q→1 with N=C12 and Q=C3×D4

Direct product G=N×Q with N=C12 and Q=C3×D4
dρLabelID
D4×C3×C12144D4xC3xC12288,815

Semidirect products G=N:Q with N=C12 and Q=C3×D4
extensionφ:Q→Aut NdρLabelID
C12⋊1(C3×D4) = C3×C12⋊D4φ: C3×D4/C6 → C22 ⊆ Aut C1296C12:1(C3xD4)288,666
C12⋊2(C3×D4) = C3×D6⋊3D4φ: C3×D4/C6 → C22 ⊆ Aut C1248C12:2(C3xD4)288,709
C12⋊3(C3×D4) = C3×C12⋊3D4φ: C3×D4/C6 → C22 ⊆ Aut C1248C12:3(C3xD4)288,711
C12⋊4(C3×D4) = C3×C4⋊D12φ: C3×D4/C12 → C2 ⊆ Aut C1296C12:4(C3xD4)288,645
C12⋊5(C3×D4) = C12×D12φ: C3×D4/C12 → C2 ⊆ Aut C1296C12:5(C3xD4)288,644
C12⋊6(C3×D4) = C32×C4⋊1D4φ: C3×D4/C12 → C2 ⊆ Aut C12144C12:6(C3xD4)288,824
C12⋊7(C3×D4) = C3×C12⋊7D4φ: C3×D4/C2×C6 → C2 ⊆ Aut C1248C12:7(C3xD4)288,701
C12⋊8(C3×D4) = C12×C3⋊D4φ: C3×D4/C2×C6 → C2 ⊆ Aut C1248C12:8(C3xD4)288,699
C12⋊9(C3×D4) = C32×C4⋊D4φ: C3×D4/C2×C6 → C2 ⊆ Aut C12144C12:9(C3xD4)288,818

Non-split extensions G=N.Q with N=C12 and Q=C3×D4
extensionφ:Q→Aut NdρLabelID
C12.1(C3×D4) = C3×C6.D8φ: C3×D4/C6 → C22 ⊆ Aut C1296C12.1(C3xD4)288,243
C12.2(C3×D4) = C3×C6.SD16φ: C3×D4/C6 → C22 ⊆ Aut C1296C12.2(C3xD4)288,244
C12.3(C3×D4) = C3×C3⋊D16φ: C3×D4/C6 → C22 ⊆ Aut C12484C12.3(C3xD4)288,260
C12.4(C3×D4) = C3×D8.S3φ: C3×D4/C6 → C22 ⊆ Aut C12484C12.4(C3xD4)288,261
C12.5(C3×D4) = C3×C8.6D6φ: C3×D4/C6 → C22 ⊆ Aut C12964C12.5(C3xD4)288,262
C12.6(C3×D4) = C3×C3⋊Q32φ: C3×D4/C6 → C22 ⊆ Aut C12964C12.6(C3xD4)288,263
C12.7(C3×D4) = C3×D4⋊Dic3φ: C3×D4/C6 → C22 ⊆ Aut C1248C12.7(C3xD4)288,266
C12.8(C3×D4) = C3×C12.D4φ: C3×D4/C6 → C22 ⊆ Aut C12244C12.8(C3xD4)288,267
C12.9(C3×D4) = C3×Q8⋊2Dic3φ: C3×D4/C6 → C22 ⊆ Aut C1296C12.9(C3xD4)288,269
C12.10(C3×D4) = C3×C12.10D4φ: C3×D4/C6 → C22 ⊆ Aut C12484C12.10(C3xD4)288,270
C12.11(C3×D4) = C3×C4.D12φ: C3×D4/C6 → C22 ⊆ Aut C1296C12.11(C3xD4)288,668
C12.12(C3×D4) = C3×C8⋊D6φ: C3×D4/C6 → C22 ⊆ Aut C12484C12.12(C3xD4)288,679
C12.13(C3×D4) = C3×C8.D6φ: C3×D4/C6 → C22 ⊆ Aut C12484C12.13(C3xD4)288,680
C12.14(C3×D4) = C6×D4⋊S3φ: C3×D4/C6 → C22 ⊆ Aut C1248C12.14(C3xD4)288,702
C12.15(C3×D4) = C3×D12⋊6C22φ: C3×D4/C6 → C22 ⊆ Aut C12244C12.15(C3xD4)288,703
C12.16(C3×D4) = C6×D4.S3φ: C3×D4/C6 → C22 ⊆ Aut C1248C12.16(C3xD4)288,704
C12.17(C3×D4) = C3×C23.12D6φ: C3×D4/C6 → C22 ⊆ Aut C1248C12.17(C3xD4)288,707
C12.18(C3×D4) = C6×Q8⋊2S3φ: C3×D4/C6 → C22 ⊆ Aut C1296C12.18(C3xD4)288,712
C12.19(C3×D4) = C3×Q8.11D6φ: C3×D4/C6 → C22 ⊆ Aut C12484C12.19(C3xD4)288,713
C12.20(C3×D4) = C6×C3⋊Q16φ: C3×D4/C6 → C22 ⊆ Aut C1296C12.20(C3xD4)288,714
C12.21(C3×D4) = C3×Dic3⋊Q8φ: C3×D4/C6 → C22 ⊆ Aut C1296C12.21(C3xD4)288,715
C12.22(C3×D4) = C3×D6⋊3Q8φ: C3×D4/C6 → C22 ⊆ Aut C1296C12.22(C3xD4)288,717
C12.23(C3×D4) = C3×C12.23D4φ: C3×D4/C6 → C22 ⊆ Aut C1296C12.23(C3xD4)288,718
C12.24(C3×D4) = C3×D48φ: C3×D4/C12 → C2 ⊆ Aut C12962C12.24(C3xD4)288,233
C12.25(C3×D4) = C3×C48⋊C2φ: C3×D4/C12 → C2 ⊆ Aut C12962C12.25(C3xD4)288,234
C12.26(C3×D4) = C3×Dic24φ: C3×D4/C12 → C2 ⊆ Aut C12962C12.26(C3xD4)288,235
C12.27(C3×D4) = C3×C12⋊2Q8φ: C3×D4/C12 → C2 ⊆ Aut C1296C12.27(C3xD4)288,640
C12.28(C3×D4) = C3×C42⋊7S3φ: C3×D4/C12 → C2 ⊆ Aut C1296C12.28(C3xD4)288,646
C12.29(C3×D4) = C6×C24⋊C2φ: C3×D4/C12 → C2 ⊆ Aut C1296C12.29(C3xD4)288,673
C12.30(C3×D4) = C6×D24φ: C3×D4/C12 → C2 ⊆ Aut C1296C12.30(C3xD4)288,674
C12.31(C3×D4) = C6×Dic12φ: C3×D4/C12 → C2 ⊆ Aut C1296C12.31(C3xD4)288,676
C12.32(C3×D4) = C3×C12⋊C8φ: C3×D4/C12 → C2 ⊆ Aut C1296C12.32(C3xD4)288,238
C12.33(C3×D4) = C3×C42⋊4S3φ: C3×D4/C12 → C2 ⊆ Aut C12242C12.33(C3xD4)288,239
C12.34(C3×D4) = C3×C24.C4φ: C3×D4/C12 → C2 ⊆ Aut C12482C12.34(C3xD4)288,253
C12.35(C3×D4) = C3×C4○D24φ: C3×D4/C12 → C2 ⊆ Aut C12482C12.35(C3xD4)288,675
C12.36(C3×D4) = C9×D16φ: C3×D4/C12 → C2 ⊆ Aut C121442C12.36(C3xD4)288,61
C12.37(C3×D4) = C9×SD32φ: C3×D4/C12 → C2 ⊆ Aut C121442C12.37(C3xD4)288,62
C12.38(C3×D4) = C9×Q32φ: C3×D4/C12 → C2 ⊆ Aut C122882C12.38(C3xD4)288,63
C12.39(C3×D4) = C9×C4.4D4φ: C3×D4/C12 → C2 ⊆ Aut C12144C12.39(C3xD4)288,174
C12.40(C3×D4) = C9×C4⋊1D4φ: C3×D4/C12 → C2 ⊆ Aut C12144C12.40(C3xD4)288,177
C12.41(C3×D4) = C9×C4⋊Q8φ: C3×D4/C12 → C2 ⊆ Aut C12288C12.41(C3xD4)288,178
C12.42(C3×D4) = D8×C18φ: C3×D4/C12 → C2 ⊆ Aut C12144C12.42(C3xD4)288,182
C12.43(C3×D4) = SD16×C18φ: C3×D4/C12 → C2 ⊆ Aut C12144C12.43(C3xD4)288,183
C12.44(C3×D4) = Q16×C18φ: C3×D4/C12 → C2 ⊆ Aut C12288C12.44(C3xD4)288,184
C12.45(C3×D4) = C32×D16φ: C3×D4/C12 → C2 ⊆ Aut C12144C12.45(C3xD4)288,329
C12.46(C3×D4) = C32×SD32φ: C3×D4/C12 → C2 ⊆ Aut C12144C12.46(C3xD4)288,330
C12.47(C3×D4) = C32×Q32φ: C3×D4/C12 → C2 ⊆ Aut C12288C12.47(C3xD4)288,331
C12.48(C3×D4) = C32×C4.4D4φ: C3×D4/C12 → C2 ⊆ Aut C12144C12.48(C3xD4)288,821
C12.49(C3×D4) = C32×C4⋊Q8φ: C3×D4/C12 → C2 ⊆ Aut C12288C12.49(C3xD4)288,825
C12.50(C3×D4) = D8×C3×C6φ: C3×D4/C12 → C2 ⊆ Aut C12144C12.50(C3xD4)288,829
C12.51(C3×D4) = SD16×C3×C6φ: C3×D4/C12 → C2 ⊆ Aut C12144C12.51(C3xD4)288,830
C12.52(C3×D4) = Q16×C3×C6φ: C3×D4/C12 → C2 ⊆ Aut C12288C12.52(C3xD4)288,831
C12.53(C3×D4) = C3×C2.Dic12φ: C3×D4/C2×C6 → C2 ⊆ Aut C1296C12.53(C3xD4)288,250
C12.54(C3×D4) = C3×C2.D24φ: C3×D4/C2×C6 → C2 ⊆ Aut C1296C12.54(C3xD4)288,255
C12.55(C3×D4) = C3×C12.46D4φ: C3×D4/C2×C6 → C2 ⊆ Aut C12484C12.55(C3xD4)288,257
C12.56(C3×D4) = C3×C12.47D4φ: C3×D4/C2×C6 → C2 ⊆ Aut C12484C12.56(C3xD4)288,258
C12.57(C3×D4) = C3×C12.48D4φ: C3×D4/C2×C6 → C2 ⊆ Aut C1248C12.57(C3xD4)288,695
C12.58(C3×D4) = C3×D4⋊D6φ: C3×D4/C2×C6 → C2 ⊆ Aut C12484C12.58(C3xD4)288,720
C12.59(C3×D4) = C3×Q8.14D6φ: C3×D4/C2×C6 → C2 ⊆ Aut C12484C12.59(C3xD4)288,722
C12.60(C3×D4) = C3×Dic3⋊C8φ: C3×D4/C2×C6 → C2 ⊆ Aut C1296C12.60(C3xD4)288,248
C12.61(C3×D4) = C3×D6⋊C8φ: C3×D4/C2×C6 → C2 ⊆ Aut C1296C12.61(C3xD4)288,254
C12.62(C3×D4) = C3×C12.53D4φ: C3×D4/C2×C6 → C2 ⊆ Aut C12484C12.62(C3xD4)288,256
C12.63(C3×D4) = C3×D12⋊C4φ: C3×D4/C2×C6 → C2 ⊆ Aut C12484C12.63(C3xD4)288,259
C12.64(C3×D4) = C3×C12.55D4φ: C3×D4/C2×C6 → C2 ⊆ Aut C1248C12.64(C3xD4)288,264
C12.65(C3×D4) = C3×Q8⋊3Dic3φ: C3×D4/C2×C6 → C2 ⊆ Aut C12484C12.65(C3xD4)288,271
C12.66(C3×D4) = C3×Q8.13D6φ: C3×D4/C2×C6 → C2 ⊆ Aut C12484C12.66(C3xD4)288,721
C12.67(C3×D4) = C9×C4.D4φ: C3×D4/C2×C6 → C2 ⊆ Aut C12724C12.67(C3xD4)288,50
C12.68(C3×D4) = C9×C4.10D4φ: C3×D4/C2×C6 → C2 ⊆ Aut C121444C12.68(C3xD4)288,51
C12.69(C3×D4) = C9×D4⋊C4φ: C3×D4/C2×C6 → C2 ⊆ Aut C12144C12.69(C3xD4)288,52
C12.70(C3×D4) = C9×Q8⋊C4φ: C3×D4/C2×C6 → C2 ⊆ Aut C12288C12.70(C3xD4)288,53
C12.71(C3×D4) = C9×C4⋊D4φ: C3×D4/C2×C6 → C2 ⊆ Aut C12144C12.71(C3xD4)288,171
C12.72(C3×D4) = C9×C22⋊Q8φ: C3×D4/C2×C6 → C2 ⊆ Aut C12144C12.72(C3xD4)288,172
C12.73(C3×D4) = C9×C8⋊C22φ: C3×D4/C2×C6 → C2 ⊆ Aut C12724C12.73(C3xD4)288,186
C12.74(C3×D4) = C9×C8.C22φ: C3×D4/C2×C6 → C2 ⊆ Aut C121444C12.74(C3xD4)288,187
C12.75(C3×D4) = C32×C4.D4φ: C3×D4/C2×C6 → C2 ⊆ Aut C1272C12.75(C3xD4)288,318
C12.76(C3×D4) = C32×C4.10D4φ: C3×D4/C2×C6 → C2 ⊆ Aut C12144C12.76(C3xD4)288,319
C12.77(C3×D4) = C32×D4⋊C4φ: C3×D4/C2×C6 → C2 ⊆ Aut C12144C12.77(C3xD4)288,320
C12.78(C3×D4) = C32×Q8⋊C4φ: C3×D4/C2×C6 → C2 ⊆ Aut C12288C12.78(C3xD4)288,321
C12.79(C3×D4) = C32×C22⋊Q8φ: C3×D4/C2×C6 → C2 ⊆ Aut C12144C12.79(C3xD4)288,819
C12.80(C3×D4) = C32×C8⋊C22φ: C3×D4/C2×C6 → C2 ⊆ Aut C1272C12.80(C3xD4)288,833
C12.81(C3×D4) = C32×C8.C22φ: C3×D4/C2×C6 → C2 ⊆ Aut C12144C12.81(C3xD4)288,834
C12.82(C3×D4) = C9×C22⋊C8central extension (φ=1)144C12.82(C3xD4)288,48
C12.83(C3×D4) = C9×C4≀C2central extension (φ=1)722C12.83(C3xD4)288,54
C12.84(C3×D4) = C9×C4⋊C8central extension (φ=1)288C12.84(C3xD4)288,55
C12.85(C3×D4) = C9×C8.C4central extension (φ=1)1442C12.85(C3xD4)288,58
C12.86(C3×D4) = D4×C36central extension (φ=1)144C12.86(C3xD4)288,168
C12.87(C3×D4) = C9×C4○D8central extension (φ=1)1442C12.87(C3xD4)288,185
C12.88(C3×D4) = C32×C22⋊C8central extension (φ=1)144C12.88(C3xD4)288,316
C12.89(C3×D4) = C32×C4≀C2central extension (φ=1)72C12.89(C3xD4)288,322
C12.90(C3×D4) = C32×C4⋊C8central extension (φ=1)288C12.90(C3xD4)288,323
C12.91(C3×D4) = C32×C8.C4central extension (φ=1)144C12.91(C3xD4)288,326
C12.92(C3×D4) = C32×C4○D8central extension (φ=1)144C12.92(C3xD4)288,832

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