Extensions 1→N→G→Q→1 with N=D₄ and Q=M₄(2)

Direct product G=NxQ with N=D₄ and Q=M₄(2)

		d	ρ	Label	ID
D₄xM₄(2)		32		D4xM4(2)	128,1666

Semidirect products G=N:Q with N=D₄ and Q=M₄(2)

extension	φ:Q→Out N	d	ρ	Label	ID
D₄:₁M₄(2) = C₈:₉D₈	φ: M₄(2)/C₈ → C₂ ⊆ Out D₄	64		D4:1M4(2)	128,313
D₄:₂M₄(2) = D₄:₂M₄(2)	φ: M₄(2)/C₈ → C₂ ⊆ Out D₄	64		D4:2M4(2)	128,318
D₄:₃M₄(2) = D₄:M₄(2)	φ: M₄(2)/C₂xC₄ → C₂ ⊆ Out D₄	32		D4:3M4(2)	128,218
D₄:₄M₄(2) = D₄:₄M₄(2)	φ: M₄(2)/C₂xC₄ → C₂ ⊆ Out D₄	64		D4:4M4(2)	128,221
D₄:₅M₄(2) = D₄:₅M₄(2)	φ: M₄(2)/C₂xC₄ → C₂ ⊆ Out D₄	32		D4:5M4(2)	128,222
D₄:₆M₄(2) = D₄:₆M₄(2)	φ: trivial image	64		D4:6M4(2)	128,1702
D₄:₇M₄(2) = D₄:₇M₄(2)	φ: trivial image	32		D4:7M4(2)	128,1706
D₄:₈M₄(2) = D₄:₈M₄(2)	φ: trivial image	64		D4:8M4(2)	128,1722

Non-split extensions G=N.Q with N=D₄ and Q=M₄(2)

extension	φ:Q→Out N	d	ρ	Label	ID
D₄.₁M₄(2) = C₈:₁₂SD₁₆	φ: M₄(2)/C₈ → C₂ ⊆ Out D₄	64		D4.1M4(2)	128,314
D₄.₂M₄(2) = D₄.M₄(2)	φ: M₄(2)/C₈ → C₂ ⊆ Out D₄	64		D4.2M4(2)	128,317
D₄.₃M₄(2) = C₄².₃₇₄D₄	φ: M₄(2)/C₂xC₄ → C₂ ⊆ Out D₄	64		D4.3M4(2)	128,220

׿

x

:

Z

F

o

wr

Q

<