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Extensions 1→N→G→Q→1 with N=C12 and Q=C2×C12

Direct product G=N×Q with N=C12 and Q=C2×C12
dρLabelID
C2×C122288C2xC12^2288,811

Semidirect products G=N:Q with N=C12 and Q=C2×C12
extensionφ:Q→Aut NdρLabelID
C12⋊1(C2×C12) = C3×S3×C4⋊C4φ: C2×C12/C6 → C22 ⊆ Aut C1296C12:1(C2xC12)288,662
C12⋊2(C2×C12) = C3×Dic3⋊5D4φ: C2×C12/C6 → C22 ⊆ Aut C1296C12:2(C2xC12)288,664
C12⋊3(C2×C12) = C3×D4×Dic3φ: C2×C12/C6 → C22 ⊆ Aut C1248C12:3(C2xC12)288,705
C12⋊4(C2×C12) = C12×D12φ: C2×C12/C12 → C2 ⊆ Aut C1296C12:4(C2xC12)288,644
C12⋊5(C2×C12) = S3×C4×C12φ: C2×C12/C12 → C2 ⊆ Aut C1296C12:5(C2xC12)288,642
C12⋊6(C2×C12) = D4×C3×C12φ: C2×C12/C12 → C2 ⊆ Aut C12144C12:6(C2xC12)288,815
C12⋊7(C2×C12) = C6×C4⋊Dic3φ: C2×C12/C2×C6 → C2 ⊆ Aut C1296C12:7(C2xC12)288,696
C12⋊8(C2×C12) = Dic3×C2×C12φ: C2×C12/C2×C6 → C2 ⊆ Aut C1296C12:8(C2xC12)288,693
C12⋊9(C2×C12) = C4⋊C4×C3×C6φ: C2×C12/C2×C6 → C2 ⊆ Aut C12288C12:9(C2xC12)288,813

Non-split extensions G=N.Q with N=C12 and Q=C2×C12
extensionφ:Q→Aut NdρLabelID
C12.1(C2×C12) = C3×C6.Q16φ: C2×C12/C6 → C22 ⊆ Aut C1296C12.1(C2xC12)288,241
C12.2(C2×C12) = C3×C12.Q8φ: C2×C12/C6 → C22 ⊆ Aut C1296C12.2(C2xC12)288,242
C12.3(C2×C12) = C3×C6.D8φ: C2×C12/C6 → C22 ⊆ Aut C1296C12.3(C2xC12)288,243
C12.4(C2×C12) = C3×C6.SD16φ: C2×C12/C6 → C22 ⊆ Aut C1296C12.4(C2xC12)288,244
C12.5(C2×C12) = C3×C12.53D4φ: C2×C12/C6 → C22 ⊆ Aut C12484C12.5(C2xC12)288,256
C12.6(C2×C12) = C3×D12⋊C4φ: C2×C12/C6 → C22 ⊆ Aut C12484C12.6(C2xC12)288,259
C12.7(C2×C12) = C3×D4⋊Dic3φ: C2×C12/C6 → C22 ⊆ Aut C1248C12.7(C2xC12)288,266
C12.8(C2×C12) = C3×Q8⋊2Dic3φ: C2×C12/C6 → C22 ⊆ Aut C1296C12.8(C2xC12)288,269
C12.9(C2×C12) = C3×Q8⋊3Dic3φ: C2×C12/C6 → C22 ⊆ Aut C12484C12.9(C2xC12)288,271
C12.10(C2×C12) = C3×Dic6⋊C4φ: C2×C12/C6 → C22 ⊆ Aut C1296C12.10(C2xC12)288,658
C12.11(C2×C12) = C3×C4⋊C4⋊7S3φ: C2×C12/C6 → C22 ⊆ Aut C1296C12.11(C2xC12)288,663
C12.12(C2×C12) = C3×S3×M4(2)φ: C2×C12/C6 → C22 ⊆ Aut C12484C12.12(C2xC12)288,677
C12.13(C2×C12) = C3×D12.C4φ: C2×C12/C6 → C22 ⊆ Aut C12484C12.13(C2xC12)288,678
C12.14(C2×C12) = C3×Q8×Dic3φ: C2×C12/C6 → C22 ⊆ Aut C1296C12.14(C2xC12)288,716
C12.15(C2×C12) = C3×D4.Dic3φ: C2×C12/C6 → C22 ⊆ Aut C12484C12.15(C2xC12)288,719
C12.16(C2×C12) = C3×C42⋊4S3φ: C2×C12/C12 → C2 ⊆ Aut C12242C12.16(C2xC12)288,239
C12.17(C2×C12) = C3×C2.Dic12φ: C2×C12/C12 → C2 ⊆ Aut C1296C12.17(C2xC12)288,250
C12.18(C2×C12) = C3×C2.D24φ: C2×C12/C12 → C2 ⊆ Aut C1296C12.18(C2xC12)288,255
C12.19(C2×C12) = C12×Dic6φ: C2×C12/C12 → C2 ⊆ Aut C1296C12.19(C2xC12)288,639
C12.20(C2×C12) = C3×C8○D12φ: C2×C12/C12 → C2 ⊆ Aut C12482C12.20(C2xC12)288,672
C12.21(C2×C12) = S3×C48φ: C2×C12/C12 → C2 ⊆ Aut C12962C12.21(C2xC12)288,231
C12.22(C2×C12) = C3×D6.C8φ: C2×C12/C12 → C2 ⊆ Aut C12962C12.22(C2xC12)288,232
C12.23(C2×C12) = C12×C3⋊C8φ: C2×C12/C12 → C2 ⊆ Aut C1296C12.23(C2xC12)288,236
C12.24(C2×C12) = C3×C42.S3φ: C2×C12/C12 → C2 ⊆ Aut C1296C12.24(C2xC12)288,237
C12.25(C2×C12) = Dic3×C24φ: C2×C12/C12 → C2 ⊆ Aut C1296C12.25(C2xC12)288,247
C12.26(C2×C12) = C3×C24⋊C4φ: C2×C12/C12 → C2 ⊆ Aut C1296C12.26(C2xC12)288,249
C12.27(C2×C12) = C3×C42⋊2S3φ: C2×C12/C12 → C2 ⊆ Aut C1296C12.27(C2xC12)288,643
C12.28(C2×C12) = S3×C2×C24φ: C2×C12/C12 → C2 ⊆ Aut C1296C12.28(C2xC12)288,670
C12.29(C2×C12) = C6×C8⋊S3φ: C2×C12/C12 → C2 ⊆ Aut C1296C12.29(C2xC12)288,671
C12.30(C2×C12) = C9×D4⋊C4φ: C2×C12/C12 → C2 ⊆ Aut C12144C12.30(C2xC12)288,52
C12.31(C2×C12) = C9×Q8⋊C4φ: C2×C12/C12 → C2 ⊆ Aut C12288C12.31(C2xC12)288,53
C12.32(C2×C12) = C9×C4≀C2φ: C2×C12/C12 → C2 ⊆ Aut C12722C12.32(C2xC12)288,54
C12.33(C2×C12) = D4×C36φ: C2×C12/C12 → C2 ⊆ Aut C12144C12.33(C2xC12)288,168
C12.34(C2×C12) = Q8×C36φ: C2×C12/C12 → C2 ⊆ Aut C12288C12.34(C2xC12)288,169
C12.35(C2×C12) = C9×C8○D4φ: C2×C12/C12 → C2 ⊆ Aut C121442C12.35(C2xC12)288,181
C12.36(C2×C12) = C32×D4⋊C4φ: C2×C12/C12 → C2 ⊆ Aut C12144C12.36(C2xC12)288,320
C12.37(C2×C12) = C32×Q8⋊C4φ: C2×C12/C12 → C2 ⊆ Aut C12288C12.37(C2xC12)288,321
C12.38(C2×C12) = C32×C4≀C2φ: C2×C12/C12 → C2 ⊆ Aut C1272C12.38(C2xC12)288,322
C12.39(C2×C12) = Q8×C3×C12φ: C2×C12/C12 → C2 ⊆ Aut C12288C12.39(C2xC12)288,816
C12.40(C2×C12) = C32×C8○D4φ: C2×C12/C12 → C2 ⊆ Aut C12144C12.40(C2xC12)288,828
C12.41(C2×C12) = C3×C8⋊Dic3φ: C2×C12/C2×C6 → C2 ⊆ Aut C1296C12.41(C2xC12)288,251
C12.42(C2×C12) = C3×C24⋊1C4φ: C2×C12/C2×C6 → C2 ⊆ Aut C1296C12.42(C2xC12)288,252
C12.43(C2×C12) = C3×C24.C4φ: C2×C12/C2×C6 → C2 ⊆ Aut C12482C12.43(C2xC12)288,253
C12.44(C2×C12) = C3×C23.26D6φ: C2×C12/C2×C6 → C2 ⊆ Aut C1248C12.44(C2xC12)288,697
C12.45(C2×C12) = C6×C3⋊C16φ: C2×C12/C2×C6 → C2 ⊆ Aut C1296C12.45(C2xC12)288,245
C12.46(C2×C12) = C3×C12.C8φ: C2×C12/C2×C6 → C2 ⊆ Aut C12482C12.46(C2xC12)288,246
C12.47(C2×C12) = C2×C6×C3⋊C8φ: C2×C12/C2×C6 → C2 ⊆ Aut C1296C12.47(C2xC12)288,691
C12.48(C2×C12) = C6×C4.Dic3φ: C2×C12/C2×C6 → C2 ⊆ Aut C1248C12.48(C2xC12)288,692
C12.49(C2×C12) = C9×C4.Q8φ: C2×C12/C2×C6 → C2 ⊆ Aut C12288C12.49(C2xC12)288,56
C12.50(C2×C12) = C9×C2.D8φ: C2×C12/C2×C6 → C2 ⊆ Aut C12288C12.50(C2xC12)288,57
C12.51(C2×C12) = C9×C8.C4φ: C2×C12/C2×C6 → C2 ⊆ Aut C121442C12.51(C2xC12)288,58
C12.52(C2×C12) = C4⋊C4×C18φ: C2×C12/C2×C6 → C2 ⊆ Aut C12288C12.52(C2xC12)288,166
C12.53(C2×C12) = C9×C42⋊C2φ: C2×C12/C2×C6 → C2 ⊆ Aut C12144C12.53(C2xC12)288,167
C12.54(C2×C12) = M4(2)×C18φ: C2×C12/C2×C6 → C2 ⊆ Aut C12144C12.54(C2xC12)288,180
C12.55(C2×C12) = C32×C4.Q8φ: C2×C12/C2×C6 → C2 ⊆ Aut C12288C12.55(C2xC12)288,324
C12.56(C2×C12) = C32×C2.D8φ: C2×C12/C2×C6 → C2 ⊆ Aut C12288C12.56(C2xC12)288,325
C12.57(C2×C12) = C32×C8.C4φ: C2×C12/C2×C6 → C2 ⊆ Aut C12144C12.57(C2xC12)288,326
C12.58(C2×C12) = M4(2)×C3×C6φ: C2×C12/C2×C6 → C2 ⊆ Aut C12144C12.58(C2xC12)288,827
C12.59(C2×C12) = C9×C8⋊C4central extension (φ=1)288C12.59(C2xC12)288,47
C12.60(C2×C12) = C9×M5(2)central extension (φ=1)1442C12.60(C2xC12)288,60
C12.61(C2×C12) = C32×C8⋊C4central extension (φ=1)288C12.61(C2xC12)288,315
C12.62(C2×C12) = C32×M5(2)central extension (φ=1)144C12.62(C2xC12)288,328
C12.63(C2×C12) = C32×C42⋊C2central extension (φ=1)144C12.63(C2xC12)288,814

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