Extensions 1→N→G→Q→1 with N=C₈○D₄ and Q=S₃

Direct product G=N×Q with N=C₈○D₄ and Q=S₃

		d	ρ	Label	ID
S₃×C₈○D₄		48	4	S3xC8oD4	192,1308

Semidirect products G=N:Q with N=C₈○D₄ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
C₈○D₄⋊₁S₃ = C₈.₄S₄	φ: S₃/C₁ → S₃ ⊆ Out C₈○D₄	32	4	C8oD4:1S3	192,965
C₈○D₄⋊₂S₃ = C₈.₃S₄	φ: S₃/C₁ → S₃ ⊆ Out C₈○D₄	32	4+	C8oD4:2S3	192,966
C₈○D₄⋊₃S₃ = CU₂(𝔽₃)	φ: S₃/C₁ → S₃ ⊆ Out C₈○D₄	32	2	C8oD4:3S3	192,963
C₈○D₄⋊₄S₃ = C₈.₅S₄	φ: S₃/C₁ → S₃ ⊆ Out C₈○D₄	32	4	C8oD4:4S3	192,964
C₈○D₄⋊₅S₃ = Q₈.₈D₁₂	φ: S₃/C₃ → C₂ ⊆ Out C₈○D₄	48	4	C8oD4:5S3	192,700
C₈○D₄⋊₆S₃ = Q₈.₉D₁₂	φ: S₃/C₃ → C₂ ⊆ Out C₈○D₄	48	4+	C8oD4:6S3	192,701
C₈○D₄⋊₇S₃ = D₄.₁₁D₁₂	φ: S₃/C₃ → C₂ ⊆ Out C₈○D₄	48	4	C8oD4:7S3	192,1310
C₈○D₄⋊₈S₃ = D₄.₁₂D₁₂	φ: S₃/C₃ → C₂ ⊆ Out C₈○D₄	48	4+	C8oD4:8S3	192,1311
C₈○D₄⋊₉S₃ = D₄.₁₃D₁₂	φ: S₃/C₃ → C₂ ⊆ Out C₈○D₄	96	4-	C8oD4:9S3	192,1312
C₈○D₄⋊₁₀S₃ = C₂₄.₁₀₀D₄	φ: S₃/C₃ → C₂ ⊆ Out C₈○D₄	48	4	C8oD4:10S3	192,703
C₈○D₄⋊₁₁S₃ = C₂₄.₅₄D₄	φ: S₃/C₃ → C₂ ⊆ Out C₈○D₄	48	4	C8oD4:11S3	192,704
C₈○D₄⋊₁₂S₃ = M₄(2)⋊₂₈D₆	φ: S₃/C₃ → C₂ ⊆ Out C₈○D₄	48	4	C8oD4:12S3	192,1309

Non-split extensions G=N.Q with N=C₈○D₄ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
C₈○D₄.₁S₃ = C₈.S₄	φ: S₃/C₁ → S₃ ⊆ Out C₈○D₄	64	4-	C8oD4.1S3	192,962
C₈○D₄.₂S₃ = C₈.₇S₄	φ: S₃/C₁ → S₃ ⊆ Out C₈○D₄	64	2	C8oD4.2S3	192,187
C₈○D₄.₃S₃ = Q₈.₁₀D₁₂	φ: S₃/C₃ → C₂ ⊆ Out C₈○D₄	96	4-	C8oD4.3S3	192,702
C₈○D₄.₄S₃ = C₂₄.₉₉D₄	φ: S₃/C₃ → C₂ ⊆ Out C₈○D₄	96	4	C8oD4.4S3	192,120
C₈○D₄.₅S₃ = C₂₄.₇₈C₂³	φ: trivial image	96	4	C8oD4.5S3	192,699

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