Extensions 1→N→G→Q→1 with N=D₄ and Q=Dic₆

Direct product G=N×Q with N=D₄ and Q=Dic₆

		d	ρ	Label	ID
D₄×Dic₆		96		D4xDic6	192,1096

Semidirect products G=N:Q with N=D₄ and Q=Dic₆

extension	φ:Q→Out N	d	ρ	Label	ID
D₄⋊₁Dic₆ = Dic₃.D₈	φ: Dic₆/Dic₃ → C₂ ⊆ Out D₄	96		D4:1Dic6	192,318
D₄⋊₂Dic₆ = D₄⋊Dic₆	φ: Dic₆/Dic₃ → C₂ ⊆ Out D₄	96		D4:2Dic6	192,320
D₄⋊₃Dic₆ = C₁₂.₅₀D₈	φ: Dic₆/C₁₂ → C₂ ⊆ Out D₄	96		D4:3Dic6	192,566
D₄⋊₄Dic₆ = C₁₂.₃₈SD₁₆	φ: Dic₆/C₁₂ → C₂ ⊆ Out D₄	96		D4:4Dic6	192,567
D₄⋊₅Dic₆ = D₄⋊₅Dic₆	φ: trivial image	96		D4:5Dic6	192,1098
D₄⋊₆Dic₆ = D₄⋊₆Dic₆	φ: trivial image	96		D4:6Dic6	192,1102

Non-split extensions G=N.Q with N=D₄ and Q=Dic₆

extension	φ:Q→Out N	d	ρ	Label	ID
D₄.₁Dic₆ = D₄.Dic₆	φ: Dic₆/Dic₃ → C₂ ⊆ Out D₄	96		D4.1Dic6	192,322
D₄.₂Dic₆ = D₄.₂Dic₆	φ: Dic₆/Dic₃ → C₂ ⊆ Out D₄	96		D4.2Dic6	192,325
D₄.₃Dic₆ = D₄.₃Dic₆	φ: Dic₆/C₁₂ → C₂ ⊆ Out D₄	96		D4.3Dic6	192,568

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁