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

Direct product G=N×Q with N=C6 and Q=C12⋊S3
dρLabelID
C6×C12⋊S3144C6xC12:S3432,712

Semidirect products G=N:Q with N=C6 and Q=C12⋊S3
extensionφ:Q→Aut NdρLabelID
C6⋊1(C12⋊S3) = C2×C33⋊12D4φ: C12⋊S3/C3×C12 → C2 ⊆ Aut C6216C6:1(C12:S3)432,722
C6⋊2(C12⋊S3) = C2×C33⋊8D4φ: C12⋊S3/C2×C3⋊S3 → C2 ⊆ Aut C672C6:2(C12:S3)432,682

Non-split extensions G=N.Q with N=C6 and Q=C12⋊S3
extensionφ:Q→Aut NdρLabelID
C6.1(C12⋊S3) = C24.D9φ: C12⋊S3/C3×C12 → C2 ⊆ Aut C6432C6.1(C12:S3)432,168
C6.2(C12⋊S3) = C24⋊D9φ: C12⋊S3/C3×C12 → C2 ⊆ Aut C6216C6.2(C12:S3)432,171
C6.3(C12⋊S3) = C72⋊1S3φ: C12⋊S3/C3×C12 → C2 ⊆ Aut C6216C6.3(C12:S3)432,172
C6.4(C12⋊S3) = C36⋊Dic3φ: C12⋊S3/C3×C12 → C2 ⊆ Aut C6432C6.4(C12:S3)432,182
C6.5(C12⋊S3) = C6.11D36φ: C12⋊S3/C3×C12 → C2 ⊆ Aut C6216C6.5(C12:S3)432,183
C6.6(C12⋊S3) = C2×C36⋊S3φ: C12⋊S3/C3×C12 → C2 ⊆ Aut C6216C6.6(C12:S3)432,382
C6.7(C12⋊S3) = C33⋊21SD16φ: C12⋊S3/C3×C12 → C2 ⊆ Aut C6216C6.7(C12:S3)432,498
C6.8(C12⋊S3) = C33⋊12D8φ: C12⋊S3/C3×C12 → C2 ⊆ Aut C6216C6.8(C12:S3)432,499
C6.9(C12⋊S3) = C33⋊12Q16φ: C12⋊S3/C3×C12 → C2 ⊆ Aut C6432C6.9(C12:S3)432,500
C6.10(C12⋊S3) = C62.147D6φ: C12⋊S3/C3×C12 → C2 ⊆ Aut C6432C6.10(C12:S3)432,505
C6.11(C12⋊S3) = C62.148D6φ: C12⋊S3/C3×C12 → C2 ⊆ Aut C6216C6.11(C12:S3)432,506
C6.12(C12⋊S3) = C33⋊8D8φ: C12⋊S3/C2×C3⋊S3 → C2 ⊆ Aut C672C6.12(C12:S3)432,438
C6.13(C12⋊S3) = C33⋊16SD16φ: C12⋊S3/C2×C3⋊S3 → C2 ⊆ Aut C6144C6.13(C12:S3)432,443
C6.14(C12⋊S3) = C33⋊17SD16φ: C12⋊S3/C2×C3⋊S3 → C2 ⊆ Aut C672C6.14(C12:S3)432,444
C6.15(C12⋊S3) = C33⋊8Q16φ: C12⋊S3/C2×C3⋊S3 → C2 ⊆ Aut C6144C6.15(C12:S3)432,447
C6.16(C12⋊S3) = C62.78D6φ: C12⋊S3/C2×C3⋊S3 → C2 ⊆ Aut C6144C6.16(C12:S3)432,450
C6.17(C12⋊S3) = C62.79D6φ: C12⋊S3/C2×C3⋊S3 → C2 ⊆ Aut C672C6.17(C12:S3)432,451
C6.18(C12⋊S3) = C62.80D6φ: C12⋊S3/C2×C3⋊S3 → C2 ⊆ Aut C6144C6.18(C12:S3)432,452
C6.19(C12⋊S3) = C62.30D6central extension (φ=1)144C6.19(C12:S3)432,188
C6.20(C12⋊S3) = C62.31D6central extension (φ=1)72C6.20(C12:S3)432,189
C6.21(C12⋊S3) = C2×He3⋊5D4central extension (φ=1)72C6.21(C12:S3)432,386
C6.22(C12⋊S3) = C3×C24⋊2S3central extension (φ=1)144C6.22(C12:S3)432,482
C6.23(C12⋊S3) = C3×C32⋊5D8central extension (φ=1)144C6.23(C12:S3)432,483
C6.24(C12⋊S3) = C3×C32⋊5Q16central extension (φ=1)144C6.24(C12:S3)432,484
C6.25(C12⋊S3) = C3×C12⋊Dic3central extension (φ=1)144C6.25(C12:S3)432,489
C6.26(C12⋊S3) = C3×C6.11D12central extension (φ=1)144C6.26(C12:S3)432,490
C6.27(C12⋊S3) = He3⋊7SD16central stem extension (φ=1)726C6.27(C12:S3)432,175
C6.28(C12⋊S3) = He3⋊5D8central stem extension (φ=1)726C6.28(C12:S3)432,176
C6.29(C12⋊S3) = He3⋊5Q16central stem extension (φ=1)1446C6.29(C12:S3)432,177

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