Extensions 1→N→G→Q→1 with N=He₃ and Q=A₄

Direct product G=N×Q with N=He₃ and Q=A₄

		d	ρ	Label	ID
A₄×He₃		36	9	A4xHe3	324,130

Semidirect products G=N:Q with N=He₃ and Q=A₄

extension	φ:Q→Out N	d	ρ	Label	ID
He₃⋊₁A₄ = He₃⋊A₄	φ: A₄/C₂² → C₃ ⊆ Out He₃	54	9	He3:1A4	324,54
He₃⋊₂A₄ = He₃⋊₂A₄	φ: A₄/C₂² → C₃ ⊆ Out He₃	36	9	He3:2A4	324,55

Non-split extensions G=N.Q with N=He₃ and Q=A₄

extension	φ:Q→Out N	d	ρ	Label	ID
He₃.A₄ = He₃.A₄	φ: A₄/C₂² → C₃ ⊆ Out He₃	54	9	He3.A4	324,53
He₃.₂A₄ = He₃.₂A₄	φ: trivial image	54	9	He3.2A4	324,129

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=He3 and Q=A4