Extensions 1→N→G→Q→1 with N=D₄×C₃² and Q=C₂

Direct product G=N×Q with N=D₄×C₃² and Q=C₂

		d	ρ	Label	ID
D₄×C₃×C₆		72		D4xC3xC6	144,179

Semidirect products G=N:Q with N=D₄×C₃² and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(D₄×C₃²)⋊₁C₂ = C₃×D₄⋊S₃	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₃²	24	4	(D4xC3^2):1C2	144,80
(D₄×C₃²)⋊₂C₂ = C₃²⋊₇D₈	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₃²	72		(D4xC3^2):2C2	144,96
(D₄×C₃²)⋊₃C₂ = C₃×S₃×D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₃²	24	4	(D4xC3^2):3C2	144,162
(D₄×C₃²)⋊₄C₂ = C₃×D₄⋊₂S₃	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₃²	24	4	(D4xC3^2):4C2	144,163
(D₄×C₃²)⋊₅C₂ = D₄×C₃⋊S₃	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₃²	36		(D4xC3^2):5C2	144,172
(D₄×C₃²)⋊₆C₂ = C₁₂.D₆	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₃²	72		(D4xC3^2):6C2	144,173
(D₄×C₃²)⋊₇C₂ = C₃²×D₈	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₃²	72		(D4xC3^2):7C2	144,106
(D₄×C₃²)⋊₈C₂ = C₃²×C₄○D₄	φ: trivial image	72		(D4xC3^2):8C2	144,181

Non-split extensions G=N.Q with N=D₄×C₃² and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(D₄×C₃²).₁C₂ = C₃×D₄.S₃	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₃²	24	4	(D4xC3^2).1C2	144,81
(D₄×C₃²).₂C₂ = C₃²⋊₉SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₃²	72		(D4xC3^2).2C2	144,97
(D₄×C₃²).₃C₂ = C₃²×SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₃²	72		(D4xC3^2).3C2	144,107

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