Extensions 1→N→G→Q→1 with N=D₆ and Q=D₆

Direct product G=N×Q with N=D₆ and Q=D₆

		d	ρ	Label	ID
C₂²×S₃²		24		C2^2xS3^2	144,192

Semidirect products G=N:Q with N=D₆ and Q=D₆

extension	φ:Q→Out N	d	ρ	Label	ID
D₆⋊₁D₆ = S₃×D₁₂	φ: D₆/S₃ → C₂ ⊆ Out D₆	24	4+	D6:1D6	144,144
D₆⋊₂D₆ = D₆⋊D₆	φ: D₆/S₃ → C₂ ⊆ Out D₆	24	4	D6:2D6	144,145
D₆⋊₃D₆ = Dic₃⋊D₆	φ: D₆/S₃ → C₂ ⊆ Out D₆	12	4+	D6:3D6	144,154
D₆⋊₄D₆ = C₂×D₆⋊S₃	φ: D₆/C₆ → C₂ ⊆ Out D₆	48		D6:4D6	144,150
D₆⋊₅D₆ = C₂×C₃⋊D₁₂	φ: D₆/C₆ → C₂ ⊆ Out D₆	24		D6:5D6	144,151
D₆⋊₆D₆ = S₃×C₃⋊D₄	φ: D₆/C₆ → C₂ ⊆ Out D₆	24	4	D6:6D6	144,153

Non-split extensions G=N.Q with N=D₆ and Q=D₆

extension	φ:Q→Out N	d	ρ	Label	ID
D₆.₁D₆ = D₁₂⋊₅S₃	φ: D₆/S₃ → C₂ ⊆ Out D₆	48	4-	D6.1D6	144,138
D₆.₂D₆ = D₁₂⋊S₃	φ: D₆/S₃ → C₂ ⊆ Out D₆	24	4	D6.2D6	144,139
D₆.₃D₆ = D₆.₃D₆	φ: D₆/S₃ → C₂ ⊆ Out D₆	24	4	D6.3D6	144,147
D₆.₄D₆ = D₆.₄D₆	φ: D₆/S₃ → C₂ ⊆ Out D₆	24	4-	D6.4D6	144,148
D₆.₅D₆ = D₆.D₆	φ: D₆/C₆ → C₂ ⊆ Out D₆	24	4	D6.5D6	144,141
D₆.₆D₆ = D₆.₆D₆	φ: D₆/C₆ → C₂ ⊆ Out D₆	24	4+	D6.6D6	144,142
D₆.₇D₆ = S₃×Dic₆	φ: trivial image	48	4-	D6.7D6	144,137
D₆.₈D₆ = C₄×S₃²	φ: trivial image	24	4	D6.8D6	144,143
D₆.₉D₆ = C₂×S₃×Dic₃	φ: trivial image	48		D6.9D6	144,146

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁