# Extensions 1→N→G→Q→1 with N=C6 and Q=S3×C12

Direct product G=N×Q with N=C6 and Q=S3×C12
dρLabelID
S3×C6×C12144S3xC6xC12432,701

Semidirect products G=N:Q with N=C6 and Q=S3×C12
extensionφ:Q→Aut NdρLabelID
C61(S3×C12) = C6×C6.D6φ: S3×C12/C3×Dic3C2 ⊆ Aut C648C6:1(S3xC12)432,654
C62(S3×C12) = C3⋊S3×C2×C12φ: S3×C12/C3×C12C2 ⊆ Aut C6144C6:2(S3xC12)432,711
C63(S3×C12) = S3×C6×Dic3φ: S3×C12/S3×C6C2 ⊆ Aut C648C6:3(S3xC12)432,651

Non-split extensions G=N.Q with N=C6 and Q=S3×C12
extensionφ:Q→Aut NdρLabelID
C6.1(S3×C12) = C3×C12.29D6φ: S3×C12/C3×Dic3C2 ⊆ Aut C6484C6.1(S3xC12)432,415
C6.2(S3×C12) = C3×C12.31D6φ: S3×C12/C3×Dic3C2 ⊆ Aut C6484C6.2(S3xC12)432,417
C6.3(S3×C12) = C3×C6.D12φ: S3×C12/C3×Dic3C2 ⊆ Aut C648C6.3(S3xC12)432,427
C6.4(S3×C12) = C3×C62.C22φ: S3×C12/C3×Dic3C2 ⊆ Aut C648C6.4(S3xC12)432,429
C6.5(S3×C12) = D9×C24φ: S3×C12/C3×C12C2 ⊆ Aut C61442C6.5(S3xC12)432,105
C6.6(S3×C12) = C3×C8⋊D9φ: S3×C12/C3×C12C2 ⊆ Aut C61442C6.6(S3xC12)432,106
C6.7(S3×C12) = C8×C32⋊C6φ: S3×C12/C3×C12C2 ⊆ Aut C6726C6.7(S3xC12)432,115
C6.8(S3×C12) = He35M4(2)φ: S3×C12/C3×C12C2 ⊆ Aut C6726C6.8(S3xC12)432,116
C6.9(S3×C12) = C8×C9⋊C6φ: S3×C12/C3×C12C2 ⊆ Aut C6726C6.9(S3xC12)432,120
C6.10(S3×C12) = C72⋊C6φ: S3×C12/C3×C12C2 ⊆ Aut C6726C6.10(S3xC12)432,121
C6.11(S3×C12) = C12×Dic9φ: S3×C12/C3×C12C2 ⊆ Aut C6144C6.11(S3xC12)432,128
C6.12(S3×C12) = C3×Dic9⋊C4φ: S3×C12/C3×C12C2 ⊆ Aut C6144C6.12(S3xC12)432,129
C6.13(S3×C12) = C3×D18⋊C4φ: S3×C12/C3×C12C2 ⊆ Aut C6144C6.13(S3xC12)432,134
C6.14(S3×C12) = C4×C32⋊C12φ: S3×C12/C3×C12C2 ⊆ Aut C6144C6.14(S3xC12)432,138
C6.15(S3×C12) = C62.19D6φ: S3×C12/C3×C12C2 ⊆ Aut C6144C6.15(S3xC12)432,139
C6.16(S3×C12) = C62.21D6φ: S3×C12/C3×C12C2 ⊆ Aut C672C6.16(S3xC12)432,141
C6.17(S3×C12) = C4×C9⋊C12φ: S3×C12/C3×C12C2 ⊆ Aut C6144C6.17(S3xC12)432,144
C6.18(S3×C12) = Dic9⋊C12φ: S3×C12/C3×C12C2 ⊆ Aut C6144C6.18(S3xC12)432,145
C6.19(S3×C12) = D18⋊C12φ: S3×C12/C3×C12C2 ⊆ Aut C672C6.19(S3xC12)432,147
C6.20(S3×C12) = D9×C2×C12φ: S3×C12/C3×C12C2 ⊆ Aut C6144C6.20(S3xC12)432,342
C6.21(S3×C12) = C2×C4×C32⋊C6φ: S3×C12/C3×C12C2 ⊆ Aut C672C6.21(S3xC12)432,349
C6.22(S3×C12) = C2×C4×C9⋊C6φ: S3×C12/C3×C12C2 ⊆ Aut C672C6.22(S3xC12)432,353
C6.23(S3×C12) = C3⋊S3×C24φ: S3×C12/C3×C12C2 ⊆ Aut C6144C6.23(S3xC12)432,480
C6.24(S3×C12) = C3×C24⋊S3φ: S3×C12/C3×C12C2 ⊆ Aut C6144C6.24(S3xC12)432,481
C6.25(S3×C12) = C12×C3⋊Dic3φ: S3×C12/C3×C12C2 ⊆ Aut C6144C6.25(S3xC12)432,487
C6.26(S3×C12) = C3×C6.Dic6φ: S3×C12/C3×C12C2 ⊆ Aut C6144C6.26(S3xC12)432,488
C6.27(S3×C12) = C3×C6.11D12φ: S3×C12/C3×C12C2 ⊆ Aut C6144C6.27(S3xC12)432,490
C6.28(S3×C12) = C3×S3×C3⋊C8φ: S3×C12/S3×C6C2 ⊆ Aut C6484C6.28(S3xC12)432,414
C6.29(S3×C12) = C3×D6.Dic3φ: S3×C12/S3×C6C2 ⊆ Aut C6484C6.29(S3xC12)432,416
C6.30(S3×C12) = C3×Dic32φ: S3×C12/S3×C6C2 ⊆ Aut C648C6.30(S3xC12)432,425
C6.31(S3×C12) = C3×D6⋊Dic3φ: S3×C12/S3×C6C2 ⊆ Aut C648C6.31(S3xC12)432,426
C6.32(S3×C12) = C3×Dic3⋊Dic3φ: S3×C12/S3×C6C2 ⊆ Aut C648C6.32(S3xC12)432,428
C6.33(S3×C12) = S3×C72central extension (φ=1)1442C6.33(S3xC12)432,109
C6.34(S3×C12) = C9×C8⋊S3central extension (φ=1)1442C6.34(S3xC12)432,110
C6.35(S3×C12) = Dic3×C36central extension (φ=1)144C6.35(S3xC12)432,131
C6.36(S3×C12) = C9×Dic3⋊C4central extension (φ=1)144C6.36(S3xC12)432,132
C6.37(S3×C12) = C9×D6⋊C4central extension (φ=1)144C6.37(S3xC12)432,135
C6.38(S3×C12) = S3×C2×C36central extension (φ=1)144C6.38(S3xC12)432,345
C6.39(S3×C12) = S3×C3×C24central extension (φ=1)144C6.39(S3xC12)432,464
C6.40(S3×C12) = C32×C8⋊S3central extension (φ=1)144C6.40(S3xC12)432,465
C6.41(S3×C12) = Dic3×C3×C12central extension (φ=1)144C6.41(S3xC12)432,471
C6.42(S3×C12) = C32×Dic3⋊C4central extension (φ=1)144C6.42(S3xC12)432,472
C6.43(S3×C12) = C32×D6⋊C4central extension (φ=1)144C6.43(S3xC12)432,474

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