Extensions 1→N→G→Q→1 with N=C₂⁴ and Q=S₃

Direct product G=N×Q with N=C₂⁴ and Q=S₃

		d	ρ	Label	ID
S₃×C₂⁴		48		S3xC2^4	96,230

Semidirect products G=N:Q with N=C₂⁴ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂⁴⋊₁S₃ = A₄⋊D₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂⁴	12	6+	C2^4:1S3	96,195
C₂⁴⋊₂S₃ = C₂²×S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂⁴	12		C2^4:2S3	96,226
C₂⁴⋊₃S₃ = C₂²⋊S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂⁴	8	6+	C2^4:3S3	96,227
C₂⁴⋊₄S₃ = C₂⁴⋊₄S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₂⁴	24		C2^4:4S3	96,160
C₂⁴⋊₅S₃ = C₂²×C₃⋊D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂⁴	48		C2^4:5S3	96,219

Non-split extensions G=N.Q with N=C₂⁴ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂⁴.S₃ = C₂×A₄⋊C₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂⁴	24		C2^4.S3	96,194
C₂⁴.₂S₃ = C₂×C₆.D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂⁴	48		C2^4.2S3	96,159
C₂⁴.₃S₃ = C₂³×Dic₃	central extension (φ=1)	96		C2^4.3S3	96,218

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