Extensions 1→N→G→Q→1 with N=C₂³⋊C₄ and Q=S₃

Direct product G=N×Q with N=C₂³⋊C₄ and Q=S₃

		d	ρ	Label	ID
S₃×C₂³⋊C₄		24	8+	S3xC2^3:C4	192,302

Semidirect products G=N:Q with N=C₂³⋊C₄ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
C₂³⋊C₄⋊₁S₃ = C₃⋊C₂≀C₄	φ: S₃/C₃ → C₂ ⊆ Out C₂³⋊C₄	24	8+	C2^3:C4:1S3	192,30
C₂³⋊C₄⋊₂S₃ = C₂³.₂D₁₂	φ: S₃/C₃ → C₂ ⊆ Out C₂³⋊C₄	24	8+	C2^3:C4:2S3	192,33
C₂³⋊C₄⋊₃S₃ = C₂³⋊D₁₂	φ: S₃/C₃ → C₂ ⊆ Out C₂³⋊C₄	24	8+	C2^3:C4:3S3	192,300
C₂³⋊C₄⋊₄S₃ = C₂³.₅D₁₂	φ: S₃/C₃ → C₂ ⊆ Out C₂³⋊C₄	48	8-	C2^3:C4:4S3	192,301
C₂³⋊C₄⋊₅S₃ = C₂³⋊C₄⋊₅S₃	φ: trivial image	48	8-	C2^3:C4:5S3	192,299

Non-split extensions G=N.Q with N=C₂³⋊C₄ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
C₂³⋊C₄.₁S₃ = (C₂×D₄).D₆	φ: S₃/C₃ → C₂ ⊆ Out C₂³⋊C₄	48	8-	C2^3:C4.1S3	192,31
C₂³⋊C₄.₂S₃ = C₂³.D₁₂	φ: S₃/C₃ → C₂ ⊆ Out C₂³⋊C₄	48	8-	C2^3:C4.2S3	192,32

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁