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

Direct product G=N×Q with N=He₃⋊C₃ and Q=S₃

		d	ρ	Label	ID
S₃×He₃⋊C₃		54	6	S3xHe3:C3	486,123

Semidirect products G=N:Q with N=He₃⋊C₃ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
He₃⋊C₃⋊S₃ = C₉²⋊₂S₃	φ: S₃/C₁ → S₃ ⊆ Out He₃⋊C₃	27	3	He3:C3:S3	486,61
He₃⋊C₃⋊₂S₃ = He₃⋊C₃⋊₂S₃	φ: S₃/C₃ → C₂ ⊆ Out He₃⋊C₃	54	6	He3:C3:2S3	486,172
He₃⋊C₃⋊₃S₃ = He₃⋊C₃⋊₃S₃	φ: S₃/C₃ → C₂ ⊆ Out He₃⋊C₃	81		He3:C3:3S3	486,173
He₃⋊C₃⋊₄S₃ = C₃≀C₃.S₃	φ: S₃/C₃ → C₂ ⊆ Out He₃⋊C₃	27	6+	He3:C3:4S3	486,175
He₃⋊C₃⋊₅S₃ = C₃⋊(He₃⋊S₃)	φ: S₃/C₃ → C₂ ⊆ Out He₃⋊C₃	81		He3:C3:5S3	486,187
He₃⋊C₃⋊₆S₃ = C₃≀C₃⋊S₃	φ: S₃/C₃ → C₂ ⊆ Out He₃⋊C₃	27	6+	He3:C3:6S3	486,189

Non-split extensions G=N.Q with N=He₃⋊C₃ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
He₃⋊C₃.₁S₃ = C₉²⋊C₆	φ: S₃/C₁ → S₃ ⊆ Out He₃⋊C₃	27	6+	He3:C3.1S3	486,35
He₃⋊C₃.₂S₃ = C₉²⋊₂C₆	φ: S₃/C₁ → S₃ ⊆ Out He₃⋊C₃	27	6+	He3:C3.2S3	486,37

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