Extensions 1→N→G→Q→1 with N=D₄⋊C₄ and Q=S₃

Direct product G=N×Q with N=D₄⋊C₄ and Q=S₃

		d	ρ	Label	ID
S₃×D₄⋊C₄		48		S3xD4:C4	192,328

Semidirect products G=N:Q with N=D₄⋊C₄ and Q=S₃

extension	φ:Q→Out N	d	Label	ID
D₄⋊C₄⋊₁S₃ = Dic₃.SD₁₆	φ: S₃/C₃ → C₂ ⊆ Out D₄⋊C₄	96	D4:C4:1S3	192,319
D₄⋊C₄⋊₂S₃ = D₆⋊D₈	φ: S₃/C₃ → C₂ ⊆ Out D₄⋊C₄	96	D4:C4:2S3	192,334
D₄⋊C₄⋊₃S₃ = D₆⋊SD₁₆	φ: S₃/C₃ → C₂ ⊆ Out D₄⋊C₄	96	D4:C4:3S3	192,337
D₄⋊C₄⋊₄S₃ = D₄⋊D₁₂	φ: S₃/C₃ → C₂ ⊆ Out D₄⋊C₄	48	D4:C4:4S3	192,332
D₄⋊C₄⋊₅S₃ = D₆.D₈	φ: S₃/C₃ → C₂ ⊆ Out D₄⋊C₄	96	D4:C4:5S3	192,333
D₄⋊C₄⋊₆S₃ = D₄.D₁₂	φ: S₃/C₃ → C₂ ⊆ Out D₄⋊C₄	96	D4:C4:6S3	192,342
D₄⋊C₄⋊₇S₃ = C₂₄⋊₁C₄⋊C₂	φ: S₃/C₃ → C₂ ⊆ Out D₄⋊C₄	96	D4:C4:7S3	192,343
D₄⋊C₄⋊₈S₃ = D₁₂⋊₃D₄	φ: S₃/C₃ → C₂ ⊆ Out D₄⋊C₄	96	D4:C4:8S3	192,345
D₄⋊C₄⋊₉S₃ = Dic₆⋊₂D₄	φ: S₃/C₃ → C₂ ⊆ Out D₄⋊C₄	96	D4:C4:9S3	192,321
D₄⋊C₄⋊₁₀S₃ = D₆⋊₅SD₁₆	φ: S₃/C₃ → C₂ ⊆ Out D₄⋊C₄	48	D4:C4:10S3	192,335
D₄⋊C₄⋊₁₁S₃ = D₆.SD₁₆	φ: S₃/C₃ → C₂ ⊆ Out D₄⋊C₄	96	D4:C4:11S3	192,336
D₄⋊C₄⋊₁₂S₃ = D₆⋊C₈⋊₁₁C₂	φ: S₃/C₃ → C₂ ⊆ Out D₄⋊C₄	96	D4:C4:12S3	192,338
D₄⋊C₄⋊₁₃S₃ = D₄⋊₃D₁₂	φ: S₃/C₃ → C₂ ⊆ Out D₄⋊C₄	96	D4:C4:13S3	192,340
D₄⋊C₄⋊₁₄S₃ = D₁₂.D₄	φ: S₃/C₃ → C₂ ⊆ Out D₄⋊C₄	96	D4:C4:14S3	192,346
D₄⋊C₄⋊₁₅S₃ = C₄⋊C₄.D₆	φ: S₃/C₃ → C₂ ⊆ Out D₄⋊C₄	96	D4:C4:15S3	192,323
D₄⋊C₄⋊₁₆S₃ = C₄⋊C₄⋊₁₉D₆	φ: S₃/C₃ → C₂ ⊆ Out D₄⋊C₄	48	D4:C4:16S3	192,329
D₄⋊C₄⋊₁₇S₃ = D₄⋊(C₄×S₃)	φ: S₃/C₃ → C₂ ⊆ Out D₄⋊C₄	96	D4:C4:17S3	192,330
D₄⋊C₄⋊₁₈S₃ = C₃⋊C₈⋊₁D₄	φ: S₃/C₃ → C₂ ⊆ Out D₄⋊C₄	96	D4:C4:18S3	192,339
D₄⋊C₄⋊₁₉S₃ = C₃⋊C₈⋊D₄	φ: S₃/C₃ → C₂ ⊆ Out D₄⋊C₄	96	D4:C4:19S3	192,341
D₄⋊C₄⋊₂₀S₃ = D₄⋊S₃⋊C₄	φ: S₃/C₃ → C₂ ⊆ Out D₄⋊C₄	96	D4:C4:20S3	192,344
D₄⋊C₄⋊₂₁S₃ = Dic₃⋊₄D₈	φ: trivial image	96	D4:C4:21S3	192,315
D₄⋊C₄⋊₂₂S₃ = D₄⋊₂S₃⋊C₄	φ: trivial image	96	D4:C4:22S3	192,331

Non-split extensions G=N.Q with N=D₄⋊C₄ and Q=S₃

extension	φ:Q→Out N	d	Label	ID
D₄⋊C₄.₁S₃ = (C₂×C₈).₂₀₀D₆	φ: S₃/C₃ → C₂ ⊆ Out D₄⋊C₄	96	D4:C4.1S3	192,327
D₄⋊C₄.₂S₃ = Dic₃.D₈	φ: S₃/C₃ → C₂ ⊆ Out D₄⋊C₄	96	D4:C4.2S3	192,318
D₄⋊C₄.₃S₃ = D₄.₂Dic₆	φ: S₃/C₃ → C₂ ⊆ Out D₄⋊C₄	96	D4:C4.3S3	192,325
D₄⋊C₄.₄S₃ = Dic₆.D₄	φ: S₃/C₃ → C₂ ⊆ Out D₄⋊C₄	96	D4:C4.4S3	192,326
D₄⋊C₄.₅S₃ = D₄⋊Dic₆	φ: S₃/C₃ → C₂ ⊆ Out D₄⋊C₄	96	D4:C4.5S3	192,320
D₄⋊C₄.₆S₃ = D₄.Dic₆	φ: S₃/C₃ → C₂ ⊆ Out D₄⋊C₄	96	D4:C4.6S3	192,322
D₄⋊C₄.₇S₃ = D₄.S₃⋊C₄	φ: S₃/C₃ → C₂ ⊆ Out D₄⋊C₄	96	D4:C4.7S3	192,316
D₄⋊C₄.₈S₃ = C₁₂⋊Q₈⋊C₂	φ: S₃/C₃ → C₂ ⊆ Out D₄⋊C₄	96	D4:C4.8S3	192,324
D₄⋊C₄.₉S₃ = Dic₃⋊₆SD₁₆	φ: trivial image	96	D4:C4.9S3	192,317

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Extensions 1→N→G→Q→1 with N=D4⋊C4 and Q=S3

Extensions 1→N→G→Q→1 with N=D₄⋊C₄ and Q=S₃