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Extensions 1→N→G→Q→1 with N=He3 and Q=C3⋊S3

Direct product G=N×Q with N=He3 and Q=C3⋊S3
dρLabelID
C3⋊S3×He354C3:S3xHe3486,231

Semidirect products G=N:Q with N=He3 and Q=C3⋊S3
extensionφ:Q→Out NdρLabelID
He3⋊1(C3⋊S3) = C34⋊5C6φ: C3⋊S3/C3 → S3 ⊆ Out He327He3:1(C3:S3)486,167
He3⋊2(C3⋊S3) = C34⋊7S3φ: C3⋊S3/C3 → S3 ⊆ Out He327He3:2(C3:S3)486,185
He3⋊3(C3⋊S3) = C3⋊(He3⋊S3)φ: C3⋊S3/C3 → S3 ⊆ Out He381He3:3(C3:S3)486,187
He3⋊4(C3⋊S3) = C34⋊10C6φ: C3⋊S3/C32 → C2 ⊆ Out He381He3:4(C3:S3)486,242
He3⋊5(C3⋊S3) = C34⋊13S3φ: C3⋊S3/C32 → C2 ⊆ Out He354He3:5(C3:S3)486,248
He3⋊6(C3⋊S3) = 3+ 1+4⋊3C2φ: C3⋊S3/C32 → C2 ⊆ Out He3279He3:6(C3:S3)486,249

Non-split extensions G=N.Q with N=He3 and Q=C3⋊S3
extensionφ:Q→Out NdρLabelID
He3.1(C3⋊S3) = C32⋊4D9⋊C3φ: C3⋊S3/C3 → S3 ⊆ Out He381He3.1(C3:S3)486,170
He3.2(C3⋊S3) = He3⋊C3⋊3S3φ: C3⋊S3/C3 → S3 ⊆ Out He381He3.2(C3:S3)486,173
He3.3(C3⋊S3) = C3≀C3.S3φ: C3⋊S3/C3 → S3 ⊆ Out He3276+He3.3(C3:S3)486,175
He3.4(C3⋊S3) = He3.(C3⋊S3)φ: C3⋊S3/C3 → S3 ⊆ Out He381He3.4(C3:S3)486,186
He3.5(C3⋊S3) = C3≀C3⋊S3φ: C3⋊S3/C3 → S3 ⊆ Out He3276+He3.5(C3:S3)486,189
He3.6(C3⋊S3) = C9○He3⋊3S3φ: C3⋊S3/C32 → C2 ⊆ Out He381He3.6(C3:S3)486,245
He3.7(C3⋊S3) = 3+ 1+4⋊2C2φ: trivial image279He3.7(C3:S3)486,237

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