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

Direct product G=N×Q with N=C6 and Q=C6×C12
dρLabelID
C62×C12432C6^2xC12432,730

Semidirect products G=N:Q with N=C6 and Q=C6×C12
extensionφ:Q→Aut NdρLabelID
C61(C6×C12) = S3×C6×C12φ: C6×C12/C3×C12C2 ⊆ Aut C6144C6:1(C6xC12)432,701
C62(C6×C12) = Dic3×C62φ: C6×C12/C62C2 ⊆ Aut C6144C6:2(C6xC12)432,708

Non-split extensions G=N.Q with N=C6 and Q=C6×C12
extensionφ:Q→Aut NdρLabelID
C6.1(C6×C12) = S3×C3×C24φ: C6×C12/C3×C12C2 ⊆ Aut C6144C6.1(C6xC12)432,464
C6.2(C6×C12) = C32×C8⋊S3φ: C6×C12/C3×C12C2 ⊆ Aut C6144C6.2(C6xC12)432,465
C6.3(C6×C12) = Dic3×C3×C12φ: C6×C12/C3×C12C2 ⊆ Aut C6144C6.3(C6xC12)432,471
C6.4(C6×C12) = C32×Dic3⋊C4φ: C6×C12/C3×C12C2 ⊆ Aut C6144C6.4(C6xC12)432,472
C6.5(C6×C12) = C32×D6⋊C4φ: C6×C12/C3×C12C2 ⊆ Aut C6144C6.5(C6xC12)432,474
C6.6(C6×C12) = C3×C6×C3⋊C8φ: C6×C12/C62C2 ⊆ Aut C6144C6.6(C6xC12)432,469
C6.7(C6×C12) = C32×C4.Dic3φ: C6×C12/C62C2 ⊆ Aut C672C6.7(C6xC12)432,470
C6.8(C6×C12) = C32×C4⋊Dic3φ: C6×C12/C62C2 ⊆ Aut C6144C6.8(C6xC12)432,473
C6.9(C6×C12) = C32×C6.D4φ: C6×C12/C62C2 ⊆ Aut C672C6.9(C6xC12)432,479
C6.10(C6×C12) = C42×He3central extension (φ=1)144C6.10(C6xC12)432,201
C6.11(C6×C12) = C42×3- 1+2central extension (φ=1)144C6.11(C6xC12)432,202
C6.12(C6×C12) = C22⋊C4×C3×C9central extension (φ=1)216C6.12(C6xC12)432,203
C6.13(C6×C12) = C4⋊C4×C3×C9central extension (φ=1)432C6.13(C6xC12)432,206
C6.14(C6×C12) = C2×C8×He3central extension (φ=1)144C6.14(C6xC12)432,210
C6.15(C6×C12) = C2×C8×3- 1+2central extension (φ=1)144C6.15(C6xC12)432,211
C6.16(C6×C12) = M4(2)×C3×C9central extension (φ=1)216C6.16(C6xC12)432,212
C6.17(C6×C12) = C22×C4×He3central extension (φ=1)144C6.17(C6xC12)432,401
C6.18(C6×C12) = C22×C4×3- 1+2central extension (φ=1)144C6.18(C6xC12)432,402
C6.19(C6×C12) = C22⋊C4×C33central extension (φ=1)216C6.19(C6xC12)432,513
C6.20(C6×C12) = C4⋊C4×C33central extension (φ=1)432C6.20(C6xC12)432,514
C6.21(C6×C12) = M4(2)×C33central extension (φ=1)216C6.21(C6xC12)432,516
C6.22(C6×C12) = C22⋊C4×He3central stem extension (φ=1)72C6.22(C6xC12)432,204
C6.23(C6×C12) = C22⋊C4×3- 1+2central stem extension (φ=1)72C6.23(C6xC12)432,205
C6.24(C6×C12) = C4⋊C4×He3central stem extension (φ=1)144C6.24(C6xC12)432,207
C6.25(C6×C12) = C4⋊C4×3- 1+2central stem extension (φ=1)144C6.25(C6xC12)432,208
C6.26(C6×C12) = M4(2)×He3central stem extension (φ=1)726C6.26(C6xC12)432,213
C6.27(C6×C12) = M4(2)×3- 1+2central stem extension (φ=1)726C6.27(C6xC12)432,214

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