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

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

Semidirect products G=N:Q with N=C2×C12 and Q=C3⋊S3
extensionφ:Q→Aut NdρLabelID
(C2×C12)⋊1(C3⋊S3) = C3×C6.11D12φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C12144(C2xC12):1(C3:S3)432,490
(C2×C12)⋊2(C3⋊S3) = C62.148D6φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C12216(C2xC12):2(C3:S3)432,506
(C2×C12)⋊3(C3⋊S3) = C2×C33⋊12D4φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C12216(C2xC12):3(C3:S3)432,722
(C2×C12)⋊4(C3⋊S3) = C62.160D6φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C12216(C2xC12):4(C3:S3)432,723
(C2×C12)⋊5(C3⋊S3) = C2×C4×C33⋊C2φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C12216(C2xC12):5(C3:S3)432,721
(C2×C12)⋊6(C3⋊S3) = C6×C12⋊S3φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C12144(C2xC12):6(C3:S3)432,712
(C2×C12)⋊7(C3⋊S3) = C3×C12.59D6φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C1272(C2xC12):7(C3:S3)432,713

Non-split extensions G=N.Q with N=C2×C12 and Q=C3⋊S3
extensionφ:Q→Aut NdρLabelID
(C2×C12).1(C3⋊S3) = C6.Dic18φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C12432(C2xC12).1(C3:S3)432,181
(C2×C12).2(C3⋊S3) = C6.11D36φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C12216(C2xC12).2(C3:S3)432,183
(C2×C12).3(C3⋊S3) = C62.29D6φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C12144(C2xC12).3(C3:S3)432,187
(C2×C12).4(C3⋊S3) = C62.31D6φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C1272(C2xC12).4(C3:S3)432,189
(C2×C12).5(C3⋊S3) = C3×C6.Dic6φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C12144(C2xC12).5(C3:S3)432,488
(C2×C12).6(C3⋊S3) = C62.146D6φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C12432(C2xC12).6(C3:S3)432,504
(C2×C12).7(C3⋊S3) = C36⋊Dic3φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C12432(C2xC12).7(C3:S3)432,182
(C2×C12).8(C3⋊S3) = C2×C12.D9φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C12432(C2xC12).8(C3:S3)432,380
(C2×C12).9(C3⋊S3) = C2×C36⋊S3φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C12216(C2xC12).9(C3:S3)432,382
(C2×C12).10(C3⋊S3) = C62.147D6φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C12432(C2xC12).10(C3:S3)432,505
(C2×C12).11(C3⋊S3) = C2×C33⋊8Q8φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C12432(C2xC12).11(C3:S3)432,720
(C2×C12).12(C3⋊S3) = C36.69D6φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C12216(C2xC12).12(C3:S3)432,179
(C2×C12).13(C3⋊S3) = C36.70D6φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C12216(C2xC12).13(C3:S3)432,383
(C2×C12).14(C3⋊S3) = C33⋊18M4(2)φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C12216(C2xC12).14(C3:S3)432,502
(C2×C12).15(C3⋊S3) = C2×C36.S3φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C12432(C2xC12).15(C3:S3)432,178
(C2×C12).16(C3⋊S3) = C4×C9⋊Dic3φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C12432(C2xC12).16(C3:S3)432,180
(C2×C12).17(C3⋊S3) = C2×C4×C9⋊S3φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C12216(C2xC12).17(C3:S3)432,381
(C2×C12).18(C3⋊S3) = C2×C33⋊7C8φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C12432(C2xC12).18(C3:S3)432,501
(C2×C12).19(C3⋊S3) = C4×C33⋊5C4φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C12432(C2xC12).19(C3:S3)432,503
(C2×C12).20(C3⋊S3) = He3⋊8M4(2)φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C12726(C2xC12).20(C3:S3)432,185
(C2×C12).21(C3⋊S3) = C62.30D6φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C12144(C2xC12).21(C3:S3)432,188
(C2×C12).22(C3⋊S3) = C2×He3⋊4Q8φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C12144(C2xC12).22(C3:S3)432,384
(C2×C12).23(C3⋊S3) = C2×He3⋊5D4φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C1272(C2xC12).23(C3:S3)432,386
(C2×C12).24(C3⋊S3) = C62.47D6φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C12726(C2xC12).24(C3:S3)432,387
(C2×C12).25(C3⋊S3) = C3×C12.58D6φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C1272(C2xC12).25(C3:S3)432,486
(C2×C12).26(C3⋊S3) = C3×C12⋊Dic3φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C12144(C2xC12).26(C3:S3)432,489
(C2×C12).27(C3⋊S3) = C6×C32⋊4Q8φ: C3⋊S3/C32 → C2 ⊆ Aut C2×C12144(C2xC12).27(C3:S3)432,710
(C2×C12).28(C3⋊S3) = C2×He3⋊4C8central extension (φ=1)144(C2xC12).28(C3:S3)432,184
(C2×C12).29(C3⋊S3) = C4×He3⋊3C4central extension (φ=1)144(C2xC12).29(C3:S3)432,186
(C2×C12).30(C3⋊S3) = C2×C4×He3⋊C2central extension (φ=1)72(C2xC12).30(C3:S3)432,385
(C2×C12).31(C3⋊S3) = C6×C32⋊4C8central extension (φ=1)144(C2xC12).31(C3:S3)432,485
(C2×C12).32(C3⋊S3) = C12×C3⋊Dic3central extension (φ=1)144(C2xC12).32(C3:S3)432,487

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