Extensions 1→N→G→Q→1 with N=C₄² and Q=C₂

Direct product G=N×Q with N=C₄² and Q=C₂

		d	ρ	Label	ID
C₂×C₄²		32		C2xC4^2	32,21

Semidirect products G=N:Q with N=C₄² and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄²⋊₁C₂ = C₄²⋊C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₄²	16		C4^2:1C2	32,24
C₄²⋊₂C₂ = C₄²⋊₂C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₄²	16		C4^2:2C2	32,33
C₄²⋊₃C₂ = C₄≀C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₄²	8	2	C4^2:3C2	32,11
C₄²⋊₄C₂ = C₄×D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₄²	16		C4^2:4C2	32,25
C₄²⋊₅C₂ = C₄.₄D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₄²	16		C4^2:5C2	32,31
C₄²⋊₆C₂ = C₄⋊₁D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₄²	16		C4^2:6C2	32,34

Non-split extensions G=N.Q with N=C₄² and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄².₁C₂ = C₈⋊C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₄²	32		C4^2.1C2	32,4
C₄².₂C₂ = C₄⋊C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄²	32		C4^2.2C2	32,12
C₄².₃C₂ = C₄×Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄²	32		C4^2.3C2	32,26
C₄².₄C₂ = C₄².C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₄²	32		C4^2.4C2	32,32
C₄².₅C₂ = C₄⋊Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄²	32		C4^2.5C2	32,35

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁