Extensions 1→N→G→Q→1 with N=C₄○D₁₂ and Q=S₃

Direct product G=N×Q with N=C₄○D₁₂ and Q=S₃

		d	ρ	Label	ID
S₃×C₄○D₁₂		48	4	S3xC4oD12	288,953

Semidirect products G=N:Q with N=C₄○D₁₂ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
C₄○D₁₂⋊₁S₃ = D₁₂.₂₇D₆	φ: S₃/C₃ → C₂ ⊆ Out C₄○D₁₂	48	4	C4oD12:1S3	288,477
C₄○D₁₂⋊₂S₃ = D₁₂.₃₀D₆	φ: S₃/C₃ → C₂ ⊆ Out C₄○D₁₂	48	4	C4oD12:2S3	288,470
C₄○D₁₂⋊₃S₃ = D₁₂⋊₂₀D₆	φ: S₃/C₃ → C₂ ⊆ Out C₄○D₁₂	48	4	C4oD12:3S3	288,471
C₄○D₁₂⋊₄S₃ = D₁₂⋊₁₈D₆	φ: S₃/C₃ → C₂ ⊆ Out C₄○D₁₂	24	4+	C4oD12:4S3	288,473
C₄○D₁₂⋊₅S₃ = D₁₂.₃₃D₆	φ: S₃/C₃ → C₂ ⊆ Out C₄○D₁₂	48	4	C4oD12:5S3	288,945
C₄○D₁₂⋊₆S₃ = D₁₂.₃₄D₆	φ: S₃/C₃ → C₂ ⊆ Out C₄○D₁₂	48	4-	C4oD12:6S3	288,946
C₄○D₁₂⋊₇S₃ = D₁₂⋊₂₃D₆	φ: S₃/C₃ → C₂ ⊆ Out C₄○D₁₂	24	4	C4oD12:7S3	288,954
C₄○D₁₂⋊₈S₃ = D₁₂⋊₂₄D₆	φ: S₃/C₃ → C₂ ⊆ Out C₄○D₁₂	48	4	C4oD12:8S3	288,955
C₄○D₁₂⋊₉S₃ = D₁₂⋊₂₇D₆	φ: S₃/C₃ → C₂ ⊆ Out C₄○D₁₂	24	4+	C4oD12:9S3	288,956

Non-split extensions G=N.Q with N=C₄○D₁₂ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
C₄○D₁₂.₁S₃ = D₁₂⋊₂Dic₃	φ: S₃/C₃ → C₂ ⊆ Out C₄○D₁₂	48	4	C4oD12.1S3	288,217
C₄○D₁₂.₂S₃ = D₁₂⋊₄Dic₃	φ: S₃/C₃ → C₂ ⊆ Out C₄○D₁₂	24	4	C4oD12.2S3	288,216
C₄○D₁₂.₃S₃ = D₁₂.Dic₃	φ: S₃/C₃ → C₂ ⊆ Out C₄○D₁₂	48	4	C4oD12.3S3	288,463
C₄○D₁₂.₄S₃ = D₁₂.₃₂D₆	φ: S₃/C₃ → C₂ ⊆ Out C₄○D₁₂	48	4	C4oD12.4S3	288,475
C₄○D₁₂.₅S₃ = D₁₂.₂₉D₆	φ: S₃/C₃ → C₂ ⊆ Out C₄○D₁₂	48	4-	C4oD12.5S3	288,479
C₄○D₁₂.₆S₃ = D₁₂.₂Dic₃	φ: trivial image	48	4	C4oD12.6S3	288,462

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁