Extensions 1→N→G→Q→1 with N=3_-¹⁺² and Q=S₃

Direct product G=N×Q with N=3_-¹⁺² and Q=S₃

		d	ρ	Label	ID
S₃×3_-¹⁺²		18	6	S3xES-(3,1)	162,37

Semidirect products G=N:Q with N=3_-¹⁺² and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
3_-¹⁺²⋊₁S₃ = C₃³⋊S₃	φ: S₃/C₁ → S₃ ⊆ Out 3_-¹⁺²	9	6+	ES-(3,1):1S3	162,19
3_-¹⁺²⋊₂S₃ = He₃.₃S₃	φ: S₃/C₁ → S₃ ⊆ Out 3_-¹⁺²	27	6+	ES-(3,1):2S3	162,20
3_-¹⁺²⋊₃S₃ = C₃³.S₃	φ: S₃/C₃ → C₂ ⊆ Out 3_-¹⁺²	27		ES-(3,1):3S3	162,42
3_-¹⁺²⋊₄S₃ = He₃.₄S₃	φ: S₃/C₃ → C₂ ⊆ Out 3_-¹⁺²	27	6+	ES-(3,1):4S3	162,43

Non-split extensions G=N.Q with N=3_-¹⁺² and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
3_-¹⁺².S₃ = 3_-¹⁺².S₃	φ: S₃/C₁ → S₃ ⊆ Out 3_-¹⁺²	27	6+	ES-(3,1).S3	162,22

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=3- 1+2 and Q=S3