Extensions 1→N→G→Q→1 with N=C₂×C₄ and Q=C₂×He₃

Direct product G=N×Q with N=C₂×C₄ and Q=C₂×He₃

		d	ρ	Label	ID
C₂²×C₄×He₃		144		C2^2xC4xHe3	432,401

Semidirect products G=N:Q with N=C₂×C₄ and Q=C₂×He₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₄)⋊₁(C₂×He₃) = C₂²⋊C₄×He₃	φ: C₂×He₃/He₃ → C₂ ⊆ Aut C₂×C₄	72		(C2xC4):1(C2xHe3)	432,204
(C₂×C₄)⋊₂(C₂×He₃) = C₂×D₄×He₃	φ: C₂×He₃/He₃ → C₂ ⊆ Aut C₂×C₄	72		(C2xC4):2(C2xHe3)	432,404
(C₂×C₄)⋊₃(C₂×He₃) = C₄○D₄×He₃	φ: C₂×He₃/He₃ → C₂ ⊆ Aut C₂×C₄	72	6	(C2xC4):3(C2xHe3)	432,410

Non-split extensions G=N.Q with N=C₂×C₄ and Q=C₂×He₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₄).₁(C₂×He₃) = C₄⋊C₄×He₃	φ: C₂×He₃/He₃ → C₂ ⊆ Aut C₂×C₄	144		(C2xC4).1(C2xHe3)	432,207
(C₂×C₄).₂(C₂×He₃) = M₄(2)×He₃	φ: C₂×He₃/He₃ → C₂ ⊆ Aut C₂×C₄	72	6	(C2xC4).2(C2xHe3)	432,213
(C₂×C₄).₃(C₂×He₃) = C₂×Q₈×He₃	φ: C₂×He₃/He₃ → C₂ ⊆ Aut C₂×C₄	144		(C2xC4).3(C2xHe3)	432,407
(C₂×C₄).₄(C₂×He₃) = C₄²×He₃	central extension (φ=1)	144		(C2xC4).4(C2xHe3)	432,201
(C₂×C₄).₅(C₂×He₃) = C₂×C₈×He₃	central extension (φ=1)	144		(C2xC4).5(C2xHe3)	432,210

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