Extensions 1→N→G→Q→1 with N=D₄×C₃² and Q=C₆

Direct product G=N×Q with N=D₄×C₃² and Q=C₆

		d	ρ	Label	ID
D₄×C₃²×C₆		216		D4xC3^2xC6	432,731

Semidirect products G=N:Q with N=D₄×C₃² and Q=C₆

extension	φ:Q→Out N	d	ρ	Label	ID
(D₄×C₃²)⋊₁C₆ = He₃⋊₆D₈	φ: C₆/C₁ → C₆ ⊆ Out D₄×C₃²	72	12+	(D4xC3^2):1C6	432,153
(D₄×C₃²)⋊₂C₆ = D₄×C₃²⋊C₆	φ: C₆/C₁ → C₆ ⊆ Out D₄×C₃²	36	12+	(D4xC3^2):2C6	432,360
(D₄×C₃²)⋊₃C₆ = C₆².₁₃D₆	φ: C₆/C₁ → C₆ ⊆ Out D₄×C₃²	72	12-	(D4xC3^2):3C6	432,361
(D₄×C₃²)⋊₄C₆ = D₈×He₃	φ: C₆/C₁ → C₆ ⊆ Out D₄×C₃²	72	6	(D4xC3^2):4C6	432,216
(D₄×C₃²)⋊₅C₆ = C₂×D₄×He₃	φ: C₆/C₂ → C₃ ⊆ Out D₄×C₃²	72		(D4xC3^2):5C6	432,404
(D₄×C₃²)⋊₆C₆ = C₄○D₄×He₃	φ: C₆/C₂ → C₃ ⊆ Out D₄×C₃²	72	6	(D4xC3^2):6C6	432,410
(D₄×C₃²)⋊₇C₆ = C₃²×D₄⋊S₃	φ: C₆/C₃ → C₂ ⊆ Out D₄×C₃²	72		(D4xC3^2):7C6	432,475
(D₄×C₃²)⋊₈C₆ = C₃×C₃²⋊₇D₈	φ: C₆/C₃ → C₂ ⊆ Out D₄×C₃²	72		(D4xC3^2):8C6	432,491
(D₄×C₃²)⋊₉C₆ = S₃×D₄×C₃²	φ: C₆/C₃ → C₂ ⊆ Out D₄×C₃²	72		(D4xC3^2):9C6	432,704
(D₄×C₃²)⋊₁₀C₆ = C₃²×D₄⋊₂S₃	φ: C₆/C₃ → C₂ ⊆ Out D₄×C₃²	72		(D4xC3^2):10C6	432,705
(D₄×C₃²)⋊₁₁C₆ = C₃×D₄×C₃⋊S₃	φ: C₆/C₃ → C₂ ⊆ Out D₄×C₃²	72		(D4xC3^2):11C6	432,714
(D₄×C₃²)⋊₁₂C₆ = C₃×C₁₂.D₆	φ: C₆/C₃ → C₂ ⊆ Out D₄×C₃²	72		(D4xC3^2):12C6	432,715
(D₄×C₃²)⋊₁₃C₆ = D₈×C₃³	φ: C₆/C₃ → C₂ ⊆ Out D₄×C₃²	216		(D4xC3^2):13C6	432,517
(D₄×C₃²)⋊₁₄C₆ = C₄○D₄×C₃³	φ: trivial image	216		(D4xC3^2):14C6	432,733

Non-split extensions G=N.Q with N=D₄×C₃² and Q=C₆

extension	φ:Q→Out N	d	ρ	Label	ID
(D₄×C₃²).₁C₆ = He₃⋊₈SD₁₆	φ: C₆/C₁ → C₆ ⊆ Out D₄×C₃²	72	12-	(D4xC3^2).1C6	432,152
(D₄×C₃²).₂C₆ = D₈×3_-¹⁺²	φ: C₆/C₁ → C₆ ⊆ Out D₄×C₃²	72	6	(D4xC3^2).2C6	432,217
(D₄×C₃²).₃C₆ = SD₁₆×He₃	φ: C₆/C₁ → C₆ ⊆ Out D₄×C₃²	72	6	(D4xC3^2).3C6	432,219
(D₄×C₃²).₄C₆ = SD₁₆×3_-¹⁺²	φ: C₆/C₁ → C₆ ⊆ Out D₄×C₃²	72	6	(D4xC3^2).4C6	432,220
(D₄×C₃²).₅C₆ = C₂×D₄×3_-¹⁺²	φ: C₆/C₂ → C₃ ⊆ Out D₄×C₃²	72		(D4xC3^2).5C6	432,405
(D₄×C₃²).₆C₆ = C₄○D₄×3_-¹⁺²	φ: C₆/C₂ → C₃ ⊆ Out D₄×C₃²	72	6	(D4xC3^2).6C6	432,411
(D₄×C₃²).₇C₆ = C₉×D₄⋊S₃	φ: C₆/C₃ → C₂ ⊆ Out D₄×C₃²	72	4	(D4xC3^2).7C6	432,150
(D₄×C₃²).₈C₆ = C₉×D₄.S₃	φ: C₆/C₃ → C₂ ⊆ Out D₄×C₃²	72	4	(D4xC3^2).8C6	432,151
(D₄×C₃²).₉C₆ = S₃×D₄×C₉	φ: C₆/C₃ → C₂ ⊆ Out D₄×C₃²	72	4	(D4xC3^2).9C6	432,358
(D₄×C₃²).₁₀C₆ = C₉×D₄⋊₂S₃	φ: C₆/C₃ → C₂ ⊆ Out D₄×C₃²	72	4	(D4xC3^2).10C6	432,359
(D₄×C₃²).₁₁C₆ = C₃²×D₄.S₃	φ: C₆/C₃ → C₂ ⊆ Out D₄×C₃²	72		(D4xC3^2).11C6	432,476
(D₄×C₃²).₁₂C₆ = C₃×C₃²⋊₉SD₁₆	φ: C₆/C₃ → C₂ ⊆ Out D₄×C₃²	72		(D4xC3^2).12C6	432,492
(D₄×C₃²).₁₃C₆ = D₈×C₃×C₉	φ: C₆/C₃ → C₂ ⊆ Out D₄×C₃²	216		(D4xC3^2).13C6	432,215
(D₄×C₃²).₁₄C₆ = SD₁₆×C₃×C₉	φ: C₆/C₃ → C₂ ⊆ Out D₄×C₃²	216		(D4xC3^2).14C6	432,218
(D₄×C₃²).₁₅C₆ = SD₁₆×C₃³	φ: C₆/C₃ → C₂ ⊆ Out D₄×C₃²	216		(D4xC3^2).15C6	432,518
(D₄×C₃²).₁₆C₆ = D₄×C₃×C₁₈	φ: trivial image	216		(D4xC3^2).16C6	432,403
(D₄×C₃²).₁₇C₆ = C₄○D₄×C₃×C₉	φ: trivial image	216		(D4xC3^2).17C6	432,409

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