Extensions 1→N→G→Q→1 with N=C₂²⋊C₄ and Q=C₂

Direct product G=N×Q with N=C₂²⋊C₄ and Q=C₂

		d	ρ	Label	ID
C₂×C₂²⋊C₄		16		C2xC2^2:C4	32,22

Semidirect products G=N:Q with N=C₂²⋊C₄ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
C₂²⋊C₄⋊₁C₂ = C₂³⋊C₄	φ: C₂/C₁ → C₂ ⊆ Out C₂²⋊C₄	8	4+	C2^2:C4:1C2	32,6
C₂²⋊C₄⋊₂C₂ = C₂²≀C₂	φ: C₂/C₁ → C₂ ⊆ Out C₂²⋊C₄	8		C2^2:C4:2C2	32,27
C₂²⋊C₄⋊₃C₂ = C₄⋊D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂²⋊C₄	16		C2^2:C4:3C2	32,28
C₂²⋊C₄⋊₄C₂ = C₂².D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂²⋊C₄	16		C2^2:C4:4C2	32,30
C₂²⋊C₄⋊₅C₂ = C₄.₄D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂²⋊C₄	16		C2^2:C4:5C2	32,31
C₂²⋊C₄⋊₆C₂ = C₄×D₄	φ: trivial image	16		C2^2:C4:6C2	32,25

Non-split extensions G=N.Q with N=C₂²⋊C₄ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
C₂²⋊C₄.₁C₂ = C₂²⋊Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₂²⋊C₄	16		C2^2:C4.1C2	32,29
C₂²⋊C₄.₂C₂ = C₄²⋊₂C₂	φ: C₂/C₁ → C₂ ⊆ Out C₂²⋊C₄	16		C2^2:C4.2C2	32,33
C₂²⋊C₄.₃C₂ = C₄²⋊C₂	φ: trivial image	16		C2^2:C4.3C2	32,24

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁