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Extensions 1→N→G→Q→1 with N=C12 and Q=C2×C3⋊S3

Direct product G=N×Q with N=C12 and Q=C2×C3⋊S3
dρLabelID
C3⋊S3×C2×C12144C3:S3xC2xC12432,711

Semidirect products G=N:Q with N=C12 and Q=C2×C3⋊S3
extensionφ:Q→Aut NdρLabelID
C12⋊1(C2×C3⋊S3) = S3×C12⋊S3φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C1272C12:1(C2xC3:S3)432,671
C12⋊2(C2×C3⋊S3) = C12⋊S32φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C1272C12:2(C2xC3:S3)432,673
C12⋊3(C2×C3⋊S3) = D4×C33⋊C2φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C12108C12:3(C2xC3:S3)432,724
C12⋊4(C2×C3⋊S3) = C3⋊S3×D12φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C1272C12:4(C2xC3:S3)432,672
C12⋊5(C2×C3⋊S3) = C4×S3×C3⋊S3φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C1272C12:5(C2xC3:S3)432,670
C12⋊6(C2×C3⋊S3) = C3×D4×C3⋊S3φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C1272C12:6(C2xC3:S3)432,714
C12⋊7(C2×C3⋊S3) = C2×C33⋊12D4φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C12216C12:7(C2xC3:S3)432,722
C12⋊8(C2×C3⋊S3) = C2×C4×C33⋊C2φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C12216C12:8(C2xC3:S3)432,721
C12⋊9(C2×C3⋊S3) = C6×C12⋊S3φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C12144C12:9(C2xC3:S3)432,712

Non-split extensions G=N.Q with N=C12 and Q=C2×C3⋊S3
extensionφ:Q→Aut NdρLabelID
C12.1(C2×C3⋊S3) = C36.17D6φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C12216C12.1(C2xC3:S3)432,190
C12.2(C2×C3⋊S3) = C36.18D6φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C12216C12.2(C2xC3:S3)432,191
C12.3(C2×C3⋊S3) = C36.19D6φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C12432C12.3(C2xC3:S3)432,194
C12.4(C2×C3⋊S3) = C36.20D6φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C12216C12.4(C2xC3:S3)432,195
C12.5(C2×C3⋊S3) = D4×C9⋊S3φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C12108C12.5(C2xC3:S3)432,388
C12.6(C2×C3⋊S3) = C36.27D6φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C12216C12.6(C2xC3:S3)432,389
C12.7(C2×C3⋊S3) = Q8×C9⋊S3φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C12216C12.7(C2xC3:S3)432,392
C12.8(C2×C3⋊S3) = C36.29D6φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C12216C12.8(C2xC3:S3)432,393
C12.9(C2×C3⋊S3) = C33⋊6D8φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C12144C12.9(C2xC3:S3)432,436
C12.10(C2×C3⋊S3) = C33⋊8D8φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C1272C12.10(C2xC3:S3)432,438
C12.11(C2×C3⋊S3) = C33⋊12SD16φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C12144C12.11(C2xC3:S3)432,439
C12.12(C2×C3⋊S3) = C33⋊13SD16φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C12144C12.12(C2xC3:S3)432,440
C12.13(C2×C3⋊S3) = C33⋊16SD16φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C12144C12.13(C2xC3:S3)432,443
C12.14(C2×C3⋊S3) = C33⋊17SD16φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C1272C12.14(C2xC3:S3)432,444
C12.15(C2×C3⋊S3) = C33⋊6Q16φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C12144C12.15(C2xC3:S3)432,445
C12.16(C2×C3⋊S3) = C33⋊8Q16φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C12144C12.16(C2xC3:S3)432,447
C12.17(C2×C3⋊S3) = C33⋊15D8φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C12216C12.17(C2xC3:S3)432,507
C12.18(C2×C3⋊S3) = C33⋊24SD16φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C12216C12.18(C2xC3:S3)432,508
C12.19(C2×C3⋊S3) = C33⋊27SD16φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C12216C12.19(C2xC3:S3)432,509
C12.20(C2×C3⋊S3) = C33⋊15Q16φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C12432C12.20(C2xC3:S3)432,510
C12.21(C2×C3⋊S3) = S3×C32⋊4Q8φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C12144C12.21(C2xC3:S3)432,660
C12.22(C2×C3⋊S3) = D12⋊(C3⋊S3)φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C1272C12.22(C2xC3:S3)432,662
C12.23(C2×C3⋊S3) = C12.39S32φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C1272C12.23(C2xC3:S3)432,664
C12.24(C2×C3⋊S3) = C32⋊9(S3×Q8)φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C1272C12.24(C2xC3:S3)432,666
C12.25(C2×C3⋊S3) = C12.57S32φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C12144C12.25(C2xC3:S3)432,668
C12.26(C2×C3⋊S3) = C12.58S32φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C1272C12.26(C2xC3:S3)432,669
C12.27(C2×C3⋊S3) = C62.100D6φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C12216C12.27(C2xC3:S3)432,725
C12.28(C2×C3⋊S3) = Q8×C33⋊C2φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C12216C12.28(C2xC3:S3)432,726
C12.29(C2×C3⋊S3) = (Q8×C33)⋊C2φ: C2×C3⋊S3/C32 → C22 ⊆ Aut C12216C12.29(C2xC3:S3)432,727
C12.30(C2×C3⋊S3) = C33⋊7D8φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C1272C12.30(C2xC3:S3)432,437
C12.31(C2×C3⋊S3) = C33⋊14SD16φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C12144C12.31(C2xC3:S3)432,441
C12.32(C2×C3⋊S3) = C33⋊15SD16φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C1272C12.32(C2xC3:S3)432,442
C12.33(C2×C3⋊S3) = C33⋊7Q16φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C12144C12.33(C2xC3:S3)432,446
C12.34(C2×C3⋊S3) = (C3×D12)⋊S3φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C12144C12.34(C2xC3:S3)432,661
C12.35(C2×C3⋊S3) = C3⋊S3×Dic6φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C12144C12.35(C2xC3:S3)432,663
C12.36(C2×C3⋊S3) = C12.40S32φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C1272C12.36(C2xC3:S3)432,665
C12.37(C2×C3⋊S3) = S3×C32⋊4C8φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C12144C12.37(C2xC3:S3)432,430
C12.38(C2×C3⋊S3) = C3⋊S3×C3⋊C8φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C12144C12.38(C2xC3:S3)432,431
C12.39(C2×C3⋊S3) = C12.69S32φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C1272C12.39(C2xC3:S3)432,432
C12.40(C2×C3⋊S3) = C33⋊7M4(2)φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C12144C12.40(C2xC3:S3)432,433
C12.41(C2×C3⋊S3) = C33⋊8M4(2)φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C12144C12.41(C2xC3:S3)432,434
C12.42(C2×C3⋊S3) = C33⋊9M4(2)φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C1272C12.42(C2xC3:S3)432,435
C12.43(C2×C3⋊S3) = C12.73S32φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C1272C12.43(C2xC3:S3)432,667
C12.44(C2×C3⋊S3) = He3⋊7D8φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C12726C12.44(C2xC3:S3)432,192
C12.45(C2×C3⋊S3) = He3⋊9SD16φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C12726C12.45(C2xC3:S3)432,193
C12.46(C2×C3⋊S3) = He3⋊11SD16φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C12726C12.46(C2xC3:S3)432,196
C12.47(C2×C3⋊S3) = He3⋊7Q16φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C121446C12.47(C2xC3:S3)432,197
C12.48(C2×C3⋊S3) = D4×He3⋊C2φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C12366C12.48(C2xC3:S3)432,390
C12.49(C2×C3⋊S3) = C62.16D6φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C12726C12.49(C2xC3:S3)432,391
C12.50(C2×C3⋊S3) = Q8×He3⋊C2φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C12726C12.50(C2xC3:S3)432,394
C12.51(C2×C3⋊S3) = He3⋊5D4⋊C2φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C12726C12.51(C2xC3:S3)432,395
C12.52(C2×C3⋊S3) = C3×C32⋊7D8φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C1272C12.52(C2xC3:S3)432,491
C12.53(C2×C3⋊S3) = C3×C32⋊9SD16φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C1272C12.53(C2xC3:S3)432,492
C12.54(C2×C3⋊S3) = C3×C32⋊11SD16φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C12144C12.54(C2xC3:S3)432,493
C12.55(C2×C3⋊S3) = C3×C32⋊7Q16φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C12144C12.55(C2xC3:S3)432,494
C12.56(C2×C3⋊S3) = C3×C12.D6φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C1272C12.56(C2xC3:S3)432,715
C12.57(C2×C3⋊S3) = C3×Q8×C3⋊S3φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C12144C12.57(C2xC3:S3)432,716
C12.58(C2×C3⋊S3) = C3×C12.26D6φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Aut C12144C12.58(C2xC3:S3)432,717
C12.59(C2×C3⋊S3) = C24.D9φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C12432C12.59(C2xC3:S3)432,168
C12.60(C2×C3⋊S3) = C24⋊D9φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C12216C12.60(C2xC3:S3)432,171
C12.61(C2×C3⋊S3) = C72⋊1S3φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C12216C12.61(C2xC3:S3)432,172
C12.62(C2×C3⋊S3) = C2×C12.D9φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C12432C12.62(C2xC3:S3)432,380
C12.63(C2×C3⋊S3) = C2×C36⋊S3φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C12216C12.63(C2xC3:S3)432,382
C12.64(C2×C3⋊S3) = C33⋊21SD16φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C12216C12.64(C2xC3:S3)432,498
C12.65(C2×C3⋊S3) = C33⋊12D8φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C12216C12.65(C2xC3:S3)432,499
C12.66(C2×C3⋊S3) = C33⋊12Q16φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C12432C12.66(C2xC3:S3)432,500
C12.67(C2×C3⋊S3) = C2×C33⋊8Q8φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C12432C12.67(C2xC3:S3)432,720
C12.68(C2×C3⋊S3) = C8×C9⋊S3φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C12216C12.68(C2xC3:S3)432,169
C12.69(C2×C3⋊S3) = C72⋊S3φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C12216C12.69(C2xC3:S3)432,170
C12.70(C2×C3⋊S3) = C2×C36.S3φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C12432C12.70(C2xC3:S3)432,178
C12.71(C2×C3⋊S3) = C36.69D6φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C12216C12.71(C2xC3:S3)432,179
C12.72(C2×C3⋊S3) = C2×C4×C9⋊S3φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C12216C12.72(C2xC3:S3)432,381
C12.73(C2×C3⋊S3) = C36.70D6φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C12216C12.73(C2xC3:S3)432,383
C12.74(C2×C3⋊S3) = C8×C33⋊C2φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C12216C12.74(C2xC3:S3)432,496
C12.75(C2×C3⋊S3) = C33⋊15M4(2)φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C12216C12.75(C2xC3:S3)432,497
C12.76(C2×C3⋊S3) = C2×C33⋊7C8φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C12432C12.76(C2xC3:S3)432,501
C12.77(C2×C3⋊S3) = C33⋊18M4(2)φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C12216C12.77(C2xC3:S3)432,502
C12.78(C2×C3⋊S3) = C62.160D6φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C12216C12.78(C2xC3:S3)432,723
C12.79(C2×C3⋊S3) = He3⋊7SD16φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C12726C12.79(C2xC3:S3)432,175
C12.80(C2×C3⋊S3) = He3⋊5D8φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C12726C12.80(C2xC3:S3)432,176
C12.81(C2×C3⋊S3) = He3⋊5Q16φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C121446C12.81(C2xC3:S3)432,177
C12.82(C2×C3⋊S3) = C2×He3⋊4Q8φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C12144C12.82(C2xC3:S3)432,384
C12.83(C2×C3⋊S3) = C2×He3⋊5D4φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C1272C12.83(C2xC3:S3)432,386
C12.84(C2×C3⋊S3) = C3×C24⋊2S3φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C12144C12.84(C2xC3:S3)432,482
C12.85(C2×C3⋊S3) = C3×C32⋊5D8φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C12144C12.85(C2xC3:S3)432,483
C12.86(C2×C3⋊S3) = C3×C32⋊5Q16φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C12144C12.86(C2xC3:S3)432,484
C12.87(C2×C3⋊S3) = C6×C32⋊4Q8φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Aut C12144C12.87(C2xC3:S3)432,710
C12.88(C2×C3⋊S3) = C8×He3⋊C2central extension (φ=1)723C12.88(C2xC3:S3)432,173
C12.89(C2×C3⋊S3) = He3⋊6M4(2)central extension (φ=1)726C12.89(C2xC3:S3)432,174
C12.90(C2×C3⋊S3) = C2×He3⋊4C8central extension (φ=1)144C12.90(C2xC3:S3)432,184
C12.91(C2×C3⋊S3) = He3⋊8M4(2)central extension (φ=1)726C12.91(C2xC3:S3)432,185
C12.92(C2×C3⋊S3) = C2×C4×He3⋊C2central extension (φ=1)72C12.92(C2xC3:S3)432,385
C12.93(C2×C3⋊S3) = C62.47D6central extension (φ=1)726C12.93(C2xC3:S3)432,387
C12.94(C2×C3⋊S3) = C3⋊S3×C24central extension (φ=1)144C12.94(C2xC3:S3)432,480
C12.95(C2×C3⋊S3) = C3×C24⋊S3central extension (φ=1)144C12.95(C2xC3:S3)432,481
C12.96(C2×C3⋊S3) = C6×C32⋊4C8central extension (φ=1)144C12.96(C2xC3:S3)432,485
C12.97(C2×C3⋊S3) = C3×C12.58D6central extension (φ=1)72C12.97(C2xC3:S3)432,486
C12.98(C2×C3⋊S3) = C3×C12.59D6central extension (φ=1)72C12.98(C2xC3:S3)432,713

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