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

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

		d	ρ	Label	ID
C₂²×C₄		16		C2^2xC4	16,10

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

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₄)⋊₁C₂ = C₂²⋊C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄	8		(C2xC4):1C2	16,3
(C₂×C₄)⋊₂C₂ = C₂×D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄	8		(C2xC4):2C2	16,11
(C₂×C₄)⋊₃C₂ = C₄○D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄	8	2	(C2xC4):3C2	16,13

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

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₄).₁C₂ = C₄⋊C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄	16		(C2xC4).1C2	16,4
(C₂×C₄).₂C₂ = M₄(2)	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄	8	2	(C2xC4).2C2	16,6
(C₂×C₄).₃C₂ = C₂×Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄	16		(C2xC4).3C2	16,12

⋊

ℤ

𝔽

○

≀

ℚ

◁

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