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Extensions 1→N→G→Q→1 with N=C2×C12 and Q=C3×C6

Direct product G=N×Q with N=C2×C12 and Q=C3×C6
dρLabelID
C62×C12432C6^2xC12432,730

Semidirect products G=N:Q with N=C2×C12 and Q=C3×C6
extensionφ:Q→Aut NdρLabelID
(C2×C12)⋊1(C3×C6) = C32×D6⋊C4φ: C3×C6/C32 → C2 ⊆ Aut C2×C12144(C2xC12):1(C3xC6)432,474
(C2×C12)⋊2(C3×C6) = C22⋊C4×C33φ: C3×C6/C32 → C2 ⊆ Aut C2×C12216(C2xC12):2(C3xC6)432,513
(C2×C12)⋊3(C3×C6) = C3×C6×D12φ: C3×C6/C32 → C2 ⊆ Aut C2×C12144(C2xC12):3(C3xC6)432,702
(C2×C12)⋊4(C3×C6) = C32×C4○D12φ: C3×C6/C32 → C2 ⊆ Aut C2×C1272(C2xC12):4(C3xC6)432,703
(C2×C12)⋊5(C3×C6) = S3×C6×C12φ: C3×C6/C32 → C2 ⊆ Aut C2×C12144(C2xC12):5(C3xC6)432,701
(C2×C12)⋊6(C3×C6) = D4×C32×C6φ: C3×C6/C32 → C2 ⊆ Aut C2×C12216(C2xC12):6(C3xC6)432,731
(C2×C12)⋊7(C3×C6) = C4○D4×C33φ: C3×C6/C32 → C2 ⊆ Aut C2×C12216(C2xC12):7(C3xC6)432,733

Non-split extensions G=N.Q with N=C2×C12 and Q=C3×C6
extensionφ:Q→Aut NdρLabelID
(C2×C12).1(C3×C6) = C22⋊C4×C3×C9φ: C3×C6/C32 → C2 ⊆ Aut C2×C12216(C2xC12).1(C3xC6)432,203
(C2×C12).2(C3×C6) = C22⋊C4×He3φ: C3×C6/C32 → C2 ⊆ Aut C2×C1272(C2xC12).2(C3xC6)432,204
(C2×C12).3(C3×C6) = C22⋊C4×3- 1+2φ: C3×C6/C32 → C2 ⊆ Aut C2×C1272(C2xC12).3(C3xC6)432,205
(C2×C12).4(C3×C6) = C4⋊C4×C3×C9φ: C3×C6/C32 → C2 ⊆ Aut C2×C12432(C2xC12).4(C3xC6)432,206
(C2×C12).5(C3×C6) = C4⋊C4×He3φ: C3×C6/C32 → C2 ⊆ Aut C2×C12144(C2xC12).5(C3xC6)432,207
(C2×C12).6(C3×C6) = C4⋊C4×3- 1+2φ: C3×C6/C32 → C2 ⊆ Aut C2×C12144(C2xC12).6(C3xC6)432,208
(C2×C12).7(C3×C6) = C32×Dic3⋊C4φ: C3×C6/C32 → C2 ⊆ Aut C2×C12144(C2xC12).7(C3xC6)432,472
(C2×C12).8(C3×C6) = C32×C4⋊Dic3φ: C3×C6/C32 → C2 ⊆ Aut C2×C12144(C2xC12).8(C3xC6)432,473
(C2×C12).9(C3×C6) = C3×C6×Dic6φ: C3×C6/C32 → C2 ⊆ Aut C2×C12144(C2xC12).9(C3xC6)432,700
(C2×C12).10(C3×C6) = C32×C4.Dic3φ: C3×C6/C32 → C2 ⊆ Aut C2×C1272(C2xC12).10(C3xC6)432,470
(C2×C12).11(C3×C6) = C3×C6×C3⋊C8φ: C3×C6/C32 → C2 ⊆ Aut C2×C12144(C2xC12).11(C3xC6)432,469
(C2×C12).12(C3×C6) = Dic3×C3×C12φ: C3×C6/C32 → C2 ⊆ Aut C2×C12144(C2xC12).12(C3xC6)432,471
(C2×C12).13(C3×C6) = M4(2)×C3×C9φ: C3×C6/C32 → C2 ⊆ Aut C2×C12216(C2xC12).13(C3xC6)432,212
(C2×C12).14(C3×C6) = M4(2)×He3φ: C3×C6/C32 → C2 ⊆ Aut C2×C12726(C2xC12).14(C3xC6)432,213
(C2×C12).15(C3×C6) = M4(2)×3- 1+2φ: C3×C6/C32 → C2 ⊆ Aut C2×C12726(C2xC12).15(C3xC6)432,214
(C2×C12).16(C3×C6) = D4×C3×C18φ: C3×C6/C32 → C2 ⊆ Aut C2×C12216(C2xC12).16(C3xC6)432,403
(C2×C12).17(C3×C6) = C2×D4×He3φ: C3×C6/C32 → C2 ⊆ Aut C2×C1272(C2xC12).17(C3xC6)432,404
(C2×C12).18(C3×C6) = C2×D4×3- 1+2φ: C3×C6/C32 → C2 ⊆ Aut C2×C1272(C2xC12).18(C3xC6)432,405
(C2×C12).19(C3×C6) = Q8×C3×C18φ: C3×C6/C32 → C2 ⊆ Aut C2×C12432(C2xC12).19(C3xC6)432,406
(C2×C12).20(C3×C6) = C2×Q8×He3φ: C3×C6/C32 → C2 ⊆ Aut C2×C12144(C2xC12).20(C3xC6)432,407
(C2×C12).21(C3×C6) = C2×Q8×3- 1+2φ: C3×C6/C32 → C2 ⊆ Aut C2×C12144(C2xC12).21(C3xC6)432,408
(C2×C12).22(C3×C6) = C4○D4×C3×C9φ: C3×C6/C32 → C2 ⊆ Aut C2×C12216(C2xC12).22(C3xC6)432,409
(C2×C12).23(C3×C6) = C4○D4×He3φ: C3×C6/C32 → C2 ⊆ Aut C2×C12726(C2xC12).23(C3xC6)432,410
(C2×C12).24(C3×C6) = C4○D4×3- 1+2φ: C3×C6/C32 → C2 ⊆ Aut C2×C12726(C2xC12).24(C3xC6)432,411
(C2×C12).25(C3×C6) = C4⋊C4×C33φ: C3×C6/C32 → C2 ⊆ Aut C2×C12432(C2xC12).25(C3xC6)432,514
(C2×C12).26(C3×C6) = M4(2)×C33φ: C3×C6/C32 → C2 ⊆ Aut C2×C12216(C2xC12).26(C3xC6)432,516
(C2×C12).27(C3×C6) = Q8×C32×C6φ: C3×C6/C32 → C2 ⊆ Aut C2×C12432(C2xC12).27(C3xC6)432,732
(C2×C12).28(C3×C6) = C42×He3central extension (φ=1)144(C2xC12).28(C3xC6)432,201
(C2×C12).29(C3×C6) = C42×3- 1+2central extension (φ=1)144(C2xC12).29(C3xC6)432,202
(C2×C12).30(C3×C6) = C2×C8×He3central extension (φ=1)144(C2xC12).30(C3xC6)432,210
(C2×C12).31(C3×C6) = C2×C8×3- 1+2central extension (φ=1)144(C2xC12).31(C3xC6)432,211
(C2×C12).32(C3×C6) = C22×C4×He3central extension (φ=1)144(C2xC12).32(C3xC6)432,401
(C2×C12).33(C3×C6) = C22×C4×3- 1+2central extension (φ=1)144(C2xC12).33(C3xC6)432,402

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