Extensions 1→N→G→Q→1 with N=He₃⋊C₄ and Q=C₄

Direct product G=N×Q with N=He₃⋊C₄ and Q=C₄

		d	ρ	Label	ID
C₄×He₃⋊C₄		72	3	C4xHe3:C4	432,275

Semidirect products G=N:Q with N=He₃⋊C₄ and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
He₃⋊C₄⋊₁C₄ = C₆.S₃≀C₂	φ: C₄/C₂ → C₂ ⊆ Out He₃⋊C₄	72	6-	He3:C4:1C4	432,237
He₃⋊C₄⋊₂C₄ = C₂.SU₃(𝔽₂)	φ: C₄/C₂ → C₂ ⊆ Out He₃⋊C₄	72	3	He3:C4:2C4	432,239

Non-split extensions G=N.Q with N=He₃⋊C₄ and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
He₃⋊C₄.C₄ = C₂×He₃⋊C₈	φ: C₄/C₂ → C₂ ⊆ Out He₃⋊C₄	54	6+	He3:C4.C4	432,529

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Extensions 1→N→G→Q→1 with N=He3⋊C4 and Q=C4