Extensions 1→N→G→Q→1 with N=D₄⋊C₄ and Q=C₂

Direct product G=N×Q with N=D₄⋊C₄ and Q=C₂

		d	ρ	Label	ID
C₂×D₄⋊C₄		32		C2xD4:C4	64,95

Semidirect products G=N:Q with N=D₄⋊C₄ and Q=C₂

extension	φ:Q→Out N	d	Label	ID
D₄⋊C₄⋊₁C₂ = C₈⋊₈D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄⋊C₄	32	D4:C4:1C2	64,146
D₄⋊C₄⋊₂C₂ = C₈⋊₇D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄⋊C₄	32	D4:C4:2C2	64,147
D₄⋊C₄⋊₃C₂ = C₄.₄D₈	φ: C₂/C₁ → C₂ ⊆ Out D₄⋊C₄	32	D4:C4:3C2	64,167
D₄⋊C₄⋊₄C₂ = C₂²⋊D₈	φ: C₂/C₁ → C₂ ⊆ Out D₄⋊C₄	16	D4:C4:4C2	64,128
D₄⋊C₄⋊₅C₂ = D₄.₇D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄⋊C₄	32	D4:C4:5C2	64,133
D₄⋊C₄⋊₆C₂ = C₄⋊D₈	φ: C₂/C₁ → C₂ ⊆ Out D₄⋊C₄	32	D4:C4:6C2	64,140
D₄⋊C₄⋊₇C₂ = C₂².D₈	φ: C₂/C₁ → C₂ ⊆ Out D₄⋊C₄	32	D4:C4:7C2	64,161
D₄⋊C₄⋊₈C₂ = D₄⋊D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄⋊C₄	32	D4:C4:8C2	64,130
D₄⋊C₄⋊₉C₂ = C₂²⋊SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out D₄⋊C₄	16	D4:C4:9C2	64,131
D₄⋊C₄⋊₁₀C₂ = C₄⋊SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out D₄⋊C₄	32	D4:C4:10C2	64,141
D₄⋊C₄⋊₁₁C₂ = D₄.₂D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄⋊C₄	32	D4:C4:11C2	64,144
D₄⋊C₄⋊₁₂C₂ = C₂³.₄₆D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄⋊C₄	32	D4:C4:12C2	64,162
D₄⋊C₄⋊₁₃C₂ = C₂³.₁₉D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄⋊C₄	32	D4:C4:13C2	64,163
D₄⋊C₄⋊₁₄C₂ = C₂³.₃₆D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄⋊C₄	32	D4:C4:14C2	64,98
D₄⋊C₄⋊₁₅C₂ = C₂³.₃₇D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄⋊C₄	16	D4:C4:15C2	64,99
D₄⋊C₄⋊₁₆C₂ = D₈⋊C₄	φ: C₂/C₁ → C₂ ⊆ Out D₄⋊C₄	32	D4:C4:16C2	64,123
D₄⋊C₄⋊₁₇C₂ = C₈⋊D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄⋊C₄	32	D4:C4:17C2	64,149
D₄⋊C₄⋊₁₈C₂ = C₈⋊₂D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄⋊C₄	32	D4:C4:18C2	64,150
D₄⋊C₄⋊₁₉C₂ = C₄².₂₉C₂²	φ: C₂/C₁ → C₂ ⊆ Out D₄⋊C₄	32	D4:C4:19C2	64,171
D₄⋊C₄⋊₂₀C₂ = C₂³.₂₄D₄	φ: trivial image	32	D4:C4:20C2	64,97
D₄⋊C₄⋊₂₁C₂ = C₄×D₈	φ: trivial image	32	D4:C4:21C2	64,118

Non-split extensions G=N.Q with N=D₄⋊C₄ and Q=C₂

extension	φ:Q→Out N	d	Label	ID
D₄⋊C₄.₁C₂ = C₄².₇₈C₂²	φ: C₂/C₁ → C₂ ⊆ Out D₄⋊C₄	32	D4:C4.1C2	64,169
D₄⋊C₄.₂C₂ = Q₈.D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄⋊C₄	32	D4:C4.2C2	64,145
D₄⋊C₄.₃C₂ = D₄⋊Q₈	φ: C₂/C₁ → C₂ ⊆ Out D₄⋊C₄	32	D4:C4.3C2	64,155
D₄⋊C₄.₄C₂ = D₄.Q₈	φ: C₂/C₁ → C₂ ⊆ Out D₄⋊C₄	32	D4:C4.4C2	64,159
D₄⋊C₄.₅C₂ = D₄⋊₂Q₈	φ: C₂/C₁ → C₂ ⊆ Out D₄⋊C₄	32	D4:C4.5C2	64,157
D₄⋊C₄.₆C₂ = SD₁₆⋊C₄	φ: C₂/C₁ → C₂ ⊆ Out D₄⋊C₄	32	D4:C4.6C2	64,121
D₄⋊C₄.₇C₂ = C₄².₂₈C₂²	φ: C₂/C₁ → C₂ ⊆ Out D₄⋊C₄	32	D4:C4.7C2	64,170
D₄⋊C₄.₈C₂ = C₄×SD₁₆	φ: trivial image	32	D4:C4.8C2	64,119

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=D4⋊C4 and Q=C2

Extensions 1→N→G→Q→1 with N=D₄⋊C₄ and Q=C₂