Extensions 1→N→G→Q→1 with N=D₄×C₃² and Q=C₄

Direct product G=N×Q with N=D₄×C₃² and Q=C₄

		d	ρ	Label	ID
D₄×C₃×C₁₂		144		D4xC3xC12	288,815

Semidirect products G=N:Q with N=D₄×C₃² and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
(D₄×C₃²)⋊₁C₄ = C₃⋊S₃.₅D₈	φ: C₄/C₁ → C₄ ⊆ Out D₄×C₃²	24	8+	(D4xC3^2):1C4	288,430
(D₄×C₃²)⋊₂C₄ = C₃²⋊₆C₄≀C₂	φ: C₄/C₁ → C₄ ⊆ Out D₄×C₃²	48	8-	(D4xC3^2):2C4	288,431
(D₄×C₃²)⋊₃C₄ = D₄×C₃²⋊C₄	φ: C₄/C₁ → C₄ ⊆ Out D₄×C₃²	24	8+	(D4xC3^2):3C4	288,936
(D₄×C₃²)⋊₄C₄ = C₃×D₄⋊Dic₃	φ: C₄/C₂ → C₂ ⊆ Out D₄×C₃²	48		(D4xC3^2):4C4	288,266
(D₄×C₃²)⋊₅C₄ = C₃×Q₈⋊₃Dic₃	φ: C₄/C₂ → C₂ ⊆ Out D₄×C₃²	48	4	(D4xC3^2):5C4	288,271
(D₄×C₃²)⋊₆C₄ = C₆².₁₁₆D₄	φ: C₄/C₂ → C₂ ⊆ Out D₄×C₃²	144		(D4xC3^2):6C4	288,307
(D₄×C₃²)⋊₇C₄ = C₆².₃₉D₄	φ: C₄/C₂ → C₂ ⊆ Out D₄×C₃²	72		(D4xC3^2):7C4	288,312
(D₄×C₃²)⋊₈C₄ = C₃×D₄×Dic₃	φ: C₄/C₂ → C₂ ⊆ Out D₄×C₃²	48		(D4xC3^2):8C4	288,705
(D₄×C₃²)⋊₉C₄ = D₄×C₃⋊Dic₃	φ: C₄/C₂ → C₂ ⊆ Out D₄×C₃²	144		(D4xC3^2):9C4	288,791
(D₄×C₃²)⋊₁₀C₄ = C₃²×D₄⋊C₄	φ: C₄/C₂ → C₂ ⊆ Out D₄×C₃²	144		(D4xC3^2):10C4	288,320
(D₄×C₃²)⋊₁₁C₄ = C₃²×C₄≀C₂	φ: C₄/C₂ → C₂ ⊆ Out D₄×C₃²	72		(D4xC3^2):11C4	288,322

Non-split extensions G=N.Q with N=D₄×C₃² and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
(D₄×C₃²).C₄ = C₆².(C₂×C₄)	φ: C₄/C₁ → C₄ ⊆ Out D₄×C₃²	48	8-	(D4xC3^2).C4	288,935
(D₄×C₃²).₂C₄ = C₃×D₄.Dic₃	φ: C₄/C₂ → C₂ ⊆ Out D₄×C₃²	48	4	(D4xC3^2).2C4	288,719
(D₄×C₃²).₃C₄ = D₄.(C₃⋊Dic₃)	φ: C₄/C₂ → C₂ ⊆ Out D₄×C₃²	144		(D4xC3^2).3C4	288,805
(D₄×C₃²).₄C₄ = C₃²×C₈○D₄	φ: trivial image	144		(D4xC3^2).4C4	288,828

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