C_n D_n S_n A_n ...

Extensions 1→N→G→Q→1 with N=2_-⁽¹⁺⁴⁾ and Q=S₃

Direct product G=N×Q with N=2_-⁽¹⁺⁴⁾ and Q=S₃

		d	ρ	Label	ID
S₃×2_-⁽¹⁺⁴⁾		48	8-	S3xES-(2,2)	192,1526

Semidirect products G=N:Q with N=2_-⁽¹⁺⁴⁾ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
2_-⁽¹⁺⁴⁾⋊₁S₃ = D₄.₃S₄	φ: S₃/C₁ → S₃ ⊆ Out 2_-⁽¹⁺⁴⁾	32	4	ES-(2,2):1S3	192,990
2_-⁽¹⁺⁴⁾⋊₂S₃ = D₄.₄S₄	φ: S₃/C₁ → S₃ ⊆ Out 2_-⁽¹⁺⁴⁾	16	4	ES-(2,2):2S3	192,1485
2_-⁽¹⁺⁴⁾⋊₃S₃ = D₄.₅S₄	φ: S₃/C₁ → S₃ ⊆ Out 2_-⁽¹⁺⁴⁾	32	4-	ES-(2,2):3S3	192,1486
2_-⁽¹⁺⁴⁾⋊₄S₃ = 2_-⁽¹⁺⁴⁾⋊₄S₃	φ: S₃/C₃ → C₂ ⊆ Out 2_-⁽¹⁺⁴⁾	48	8+	ES-(2,2):4S3	192,804
2_-⁽¹⁺⁴⁾⋊₅S₃ = D₁₂.₃₄C₂³	φ: S₃/C₃ → C₂ ⊆ Out 2_-⁽¹⁺⁴⁾	48	8+	ES-(2,2):5S3	192,1396
2_-⁽¹⁺⁴⁾⋊₆S₃ = D₁₂.₃₅C₂³	φ: S₃/C₃ → C₂ ⊆ Out 2_-⁽¹⁺⁴⁾	96	8-	ES-(2,2):6S3	192,1397
2_-⁽¹⁺⁴⁾⋊₇S₃ = D₁₂.₃₉C₂³	φ: trivial image	48	8+	ES-(2,2):7S3	192,1527

Non-split extensions G=N.Q with N=2_-⁽¹⁺⁴⁾ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
2_-⁽¹⁺⁴⁾.S₃ = D₄.S₄	φ: S₃/C₁ → S₃ ⊆ Out 2_-⁽¹⁺⁴⁾	32	4-	ES-(2,2).S3	192,989
2_-⁽¹⁺⁴⁾.₂S₃ = 2_-⁽¹⁺⁴⁾.₂S₃	φ: S₃/C₃ → C₂ ⊆ Out 2_-⁽¹⁺⁴⁾	48	8-	ES-(2,2).2S3	192,805

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