Extensions 1→N→G→Q→1 with N=C₃⋊S₃ and Q=S₄

Direct product G=N×Q with N=C₃⋊S₃ and Q=S₄

		d	ρ	Label	ID
C₃⋊S₃×S₄		36		C3:S3xS4	432,746

Semidirect products G=N:Q with N=C₃⋊S₃ and Q=S₄

extension	φ:Q→Out N	d	ρ	Label	ID
C₃⋊S₃⋊S₄ = C₆²⋊₅D₆	φ: S₄/C₂² → S₃ ⊆ Out C₃⋊S₃	18	6+	C3:S3:S4	432,523
C₃⋊S₃⋊₂S₄ = C₆²⋊₁₀D₆	φ: S₄/A₄ → C₂ ⊆ Out C₃⋊S₃	24	12+	C3:S3:2S4	432,748

Non-split extensions G=N.Q with N=C₃⋊S₃ and Q=S₄

extension	φ:Q→Out N	d	ρ	Label	ID
C₃⋊S₃.S₄ = AGL₂(𝔽₃)	φ: S₄/C₁ → S₄ ⊆ Out C₃⋊S₃	9	8+	C3:S3.S4	432,734
C₃⋊S₃.₂S₄ = C₆²⋊Dic₃	φ: S₄/A₄ → C₂ ⊆ Out C₃⋊S₃	24	12+	C3:S3.2S4	432,743

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C3⋊S3 and Q=S4