Extensions 1→N→G→Q→1 with N=He₃ and Q=C₆

Direct product G=N×Q with N=He₃ and Q=C₆

		d	ρ	Label	ID
C₆×He₃		54		C6xHe3	162,48

Semidirect products G=N:Q with N=He₃ and Q=C₆

extension	φ:Q→Out N	d	ρ	Label	ID
He₃⋊C₆ = C₃≀S₃	φ: C₆/C₁ → C₆ ⊆ Out He₃	9	3	He3:C6	162,10
He₃⋊₂C₆ = C₂×C₃≀C₃	φ: C₆/C₂ → C₃ ⊆ Out He₃	18	3	He3:2C6	162,28
He₃⋊₃C₆ = C₂×He₃⋊C₃	φ: C₆/C₂ → C₃ ⊆ Out He₃	54	3	He3:3C6	162,30
He₃⋊₄C₆ = C₃×C₃²⋊C₆	φ: C₆/C₃ → C₂ ⊆ Out He₃	18	6	He3:4C6	162,34
He₃⋊₅C₆ = C₃×He₃⋊C₂	φ: C₆/C₃ → C₂ ⊆ Out He₃	27		He3:5C6	162,41

Non-split extensions G=N.Q with N=He₃ and Q=C₆

extension	φ:Q→Out N	d	ρ	Label	ID
He₃.₁C₆ = He₃.C₆	φ: C₆/C₁ → C₆ ⊆ Out He₃	27	3	He3.1C6	162,12
He₃.₂C₆ = He₃.₂C₆	φ: C₆/C₁ → C₆ ⊆ Out He₃	27	3	He3.2C6	162,14
He₃.₃C₆ = C₂×He₃.C₃	φ: C₆/C₂ → C₃ ⊆ Out He₃	54	3	He3.3C6	162,29
He₃.₄C₆ = He₃.₄C₆	φ: C₆/C₃ → C₂ ⊆ Out He₃	27	3	He3.4C6	162,44
He₃.₅C₆ = C₂×C₉○He₃	φ: trivial image	54	3	He3.5C6	162,50

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