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

Direct product G=N×Q with N=He₃ and Q=S₃

		d	ρ	Label	ID
S₃×He₃		18	6	S3xHe3	162,35

Semidirect products G=N:Q with N=He₃ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
He₃⋊₁S₃ = C₃³⋊C₆	φ: S₃/C₁ → S₃ ⊆ Out He₃	9	6+	He3:1S3	162,11
He₃⋊₂S₃ = C₃³⋊S₃	φ: S₃/C₁ → S₃ ⊆ Out He₃	9	6+	He3:2S3	162,19
He₃⋊₃S₃ = He₃⋊S₃	φ: S₃/C₁ → S₃ ⊆ Out He₃	27	6+	He3:3S3	162,21
He₃⋊₄S₃ = He₃⋊₄S₃	φ: S₃/C₃ → C₂ ⊆ Out He₃	27		He3:4S3	162,40
He₃⋊₅S₃ = He₃⋊₅S₃	φ: S₃/C₃ → C₂ ⊆ Out He₃	18	6	He3:5S3	162,46

Non-split extensions G=N.Q with N=He₃ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
He₃.₁S₃ = He₃.S₃	φ: S₃/C₁ → S₃ ⊆ Out He₃	27	6+	He3.1S3	162,13
He₃.₂S₃ = He₃.₂S₃	φ: S₃/C₁ → S₃ ⊆ Out He₃	27	6+	He3.2S3	162,15
He₃.₃S₃ = He₃.₃S₃	φ: S₃/C₁ → S₃ ⊆ Out He₃	27	6+	He3.3S3	162,20
He₃.₄S₃ = He₃.₄S₃	φ: S₃/C₃ → C₂ ⊆ Out He₃	27	6+	He3.4S3	162,43

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