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

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

		d	ρ	Label	ID
C₃×He₃		27		C3xHe3	81,12

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

extension	φ:Q→Out N	d	ρ	Label	ID
He₃⋊₁C₃ = C₃≀C₃	φ: C₃/C₁ → C₃ ⊆ Out He₃	9	3	He3:1C3	81,7
He₃⋊₂C₃ = He₃⋊C₃	φ: C₃/C₁ → C₃ ⊆ Out He₃	27	3	He3:2C3	81,9

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

extension	φ:Q→Out N	d	ρ	Label	ID
He₃.C₃ = He₃.C₃	φ: C₃/C₁ → C₃ ⊆ Out He₃	27	3	He3.C3	81,8
He₃.₂C₃ = C₉○He₃	φ: trivial image	27	3	He3.2C3	81,14

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