Extensions 1→N→G→Q→1 with N=He₃ and Q=C₁₅

Direct product G=N×Q with N=He₃ and Q=C₁₅

		d	ρ	Label	ID
C₁₅×He₃		135		C15xHe3	405,12

Semidirect products G=N:Q with N=He₃ and Q=C₁₅

extension	φ:Q→Out N	d	ρ	Label	ID
He₃⋊₁C₁₅ = C₅×C₃≀C₃	φ: C₁₅/C₅ → C₃ ⊆ Out He₃	45	3	He3:1C15	405,7
He₃⋊₂C₁₅ = C₅×He₃⋊C₃	φ: C₁₅/C₅ → C₃ ⊆ Out He₃	135	3	He3:2C15	405,9

Non-split extensions G=N.Q with N=He₃ and Q=C₁₅

extension	φ:Q→Out N	d	ρ	Label	ID
He₃.C₁₅ = C₅×He₃.C₃	φ: C₁₅/C₅ → C₃ ⊆ Out He₃	135	3	He3.C15	405,8
He₃.₂C₁₅ = C₅×C₉○He₃	φ: trivial image	135	3	He3.2C15	405,14

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Extensions 1→N→G→Q→1 with N=He3 and Q=C15