Extensions 1→N→G→Q→1 with N=D₄² and Q=C₂

Direct product G=N×Q with N=D₄² and Q=C₂

		d	ρ	Label	ID
C₂×D₄²		32		C2xD4^2	128,2194

Semidirect products G=N:Q with N=D₄² and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(D₄²)⋊₁C₂ = D₄⋊D₈	φ: C₂/C₁ → C₂ ⊆ Out D₄²	32		(D4^2):1C2	128,351
(D₄²)⋊₂C₂ = C₂≀D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄²	8	4+	(D4^2):2C2	128,928
(D₄²)⋊₃C₂ = D₈⋊₉D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄²	32		(D4^2):3C2	128,1996
(D₄²)⋊₄C₂ = SD₁₆⋊D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄²	32		(D4^2):4C2	128,1997
(D₄²)⋊₅C₂ = D₈⋊₄D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄²	32		(D4^2):5C2	128,2004
(D₄²)⋊₆C₂ = SD₁₆⋊₁D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄²	32		(D4^2):6C2	128,2006
(D₄²)⋊₇C₂ = D₄×D₈	φ: C₂/C₁ → C₂ ⊆ Out D₄²	32		(D4^2):7C2	128,2011
(D₄²)⋊₈C₂ = D₄⋊₄D₈	φ: C₂/C₁ → C₂ ⊆ Out D₄²	32		(D4^2):8C2	128,2026
(D₄²)⋊₉C₂ = C₄².₅₃C₂³	φ: C₂/C₁ → C₂ ⊆ Out D₄²	32		(D4^2):9C2	128,2050
(D₄²)⋊₁₀C₂ = C₄².₄₇₄C₂³	φ: C₂/C₁ → C₂ ⊆ Out D₄²	32		(D4^2):10C2	128,2057
(D₄²)⋊₁₁C₂ = C₂².₇₃C₂⁵	φ: C₂/C₁ → C₂ ⊆ Out D₄²	16		(D4^2):11C2	128,2216
(D₄²)⋊₁₂C₂ = C₂².₇₇C₂⁵	φ: C₂/C₁ → C₂ ⊆ Out D₄²	32		(D4^2):12C2	128,2220
(D₄²)⋊₁₃C₂ = C₄⋊2₊⁽¹⁺⁴⁾	φ: C₂/C₁ → C₂ ⊆ Out D₄²	32		(D4^2):13C2	128,2228
(D₄²)⋊₁₄C₂ = C₂².₈₇C₂⁵	φ: C₂/C₁ → C₂ ⊆ Out D₄²	32		(D4^2):14C2	128,2230
(D₄²)⋊₁₅C₂ = C₂².₁₀₂C₂⁵	φ: C₂/C₁ → C₂ ⊆ Out D₄²	32		(D4^2):15C2	128,2245
(D₄²)⋊₁₆C₂ = C₂².₁₀₃C₂⁵	φ: C₂/C₁ → C₂ ⊆ Out D₄²	32		(D4^2):16C2	128,2246
(D₄²)⋊₁₇C₂ = C₂².₁₀₈C₂⁵	φ: C₂/C₁ → C₂ ⊆ Out D₄²	32		(D4^2):17C2	128,2251
(D₄²)⋊₁₈C₂ = C₄²⋊C₂³	φ: C₂/C₁ → C₂ ⊆ Out D₄²	16		(D4^2):18C2	128,2264
(D₄²)⋊₁₉C₂ = C₂².₁₂₃C₂⁵	φ: C₂/C₁ → C₂ ⊆ Out D₄²	32		(D4^2):19C2	128,2266
(D₄²)⋊₂₀C₂ = C₂².₁₂₆C₂⁵	φ: C₂/C₁ → C₂ ⊆ Out D₄²	32		(D4^2):20C2	128,2269
(D₄²)⋊₂₁C₂ = C₂².₁₃₁C₂⁵	φ: C₂/C₁ → C₂ ⊆ Out D₄²	32		(D4^2):21C2	128,2274
(D₄²)⋊₂₂C₂ = C₂².₁₃₂C₂⁵	φ: C₂/C₁ → C₂ ⊆ Out D₄²	32		(D4^2):22C2	128,2275
(D₄²)⋊₂₃C₂ = C₂².₁₃₅C₂⁵	φ: C₂/C₁ → C₂ ⊆ Out D₄²	32		(D4^2):23C2	128,2278
(D₄²)⋊₂₄C₂ = C₂².₁₃₈C₂⁵	φ: C₂/C₁ → C₂ ⊆ Out D₄²	32		(D4^2):24C2	128,2281
(D₄²)⋊₂₅C₂ = C₂².₁₄₇C₂⁵	φ: C₂/C₁ → C₂ ⊆ Out D₄²	32		(D4^2):25C2	128,2290
(D₄²)⋊₂₆C₂ = D₄×C₄○D₄	φ: trivial image	32		(D4^2):26C2	128,2200
(D₄²)⋊₂₇C₂ = C₂².₇₀C₂⁵	φ: trivial image	32		(D4^2):27C2	128,2213

Non-split extensions G=N.Q with N=D₄² and Q=C₂

extension	φ:Q→Out N	d	Label	ID
(D₄²).₁C₂ = D₄⋊₂SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out D₄²	32	(D4^2).1C2	128,361
(D₄²).₂C₂ = D₄.D₈	φ: C₂/C₁ → C₂ ⊆ Out D₄²	32	(D4^2).2C2	128,371
(D₄²).₃C₂ = D₄×SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out D₄²	32	(D4^2).3C2	128,2013
(D₄²).₄C₂ = D₄⋊₇SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out D₄²	32	(D4^2).4C2	128,2027
(D₄²).₅C₂ = C₄².₄₅C₂³	φ: C₂/C₁ → C₂ ⊆ Out D₄²	32	(D4^2).5C2	128,2042
(D₄²).₆C₂ = C₄².₄₇₃C₂³	φ: C₂/C₁ → C₂ ⊆ Out D₄²	32	(D4^2).6C2	128,2056

⋊

ℤ

𝔽

○

≀

Extensions 1→N→G→Q→1 with N=D42 and Q=C2

Extensions 1→N→G→Q→1 with N=D₄² and Q=C₂