Extensions 1→N→G→Q→1 with N=C₂×C₃²⋊C₆ and Q=C₂²

Direct product G=N×Q with N=C₂×C₃²⋊C₆ and Q=C₂²

		d	ρ	Label	ID
C₂³×C₃²⋊C₆		72		C2^3xC3^2:C6	432,558

Semidirect products G=N:Q with N=C₂×C₃²⋊C₆ and Q=C₂²

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂×C₃²⋊C₆)⋊₁C₂² = C₃⋊S₃⋊D₁₂	φ: C₂²/C₁ → C₂² ⊆ Out C₂×C₃²⋊C₆	36	12+	(C2xC3^2:C6):1C2^2	432,301
(C₂×C₃²⋊C₆)⋊₂C₂² = C₁₂.₈₆S₃²	φ: C₂²/C₁ → C₂² ⊆ Out C₂×C₃²⋊C₆	36	6+	(C2xC3^2:C6):2C2^2	432,302
(C₂×C₃²⋊C₆)⋊₃C₂² = C₆²⋊₂D₆	φ: C₂²/C₁ → C₂² ⊆ Out C₂×C₃²⋊C₆	36	6	(C2xC3^2:C6):3C2^2	432,324
(C₂×C₃²⋊C₆)⋊₄C₂² = C₂×He₃⋊₂D₄	φ: C₂²/C₂ → C₂ ⊆ Out C₂×C₃²⋊C₆	72		(C2xC3^2:C6):4C2^2	432,320
(C₂×C₃²⋊C₆)⋊₅C₂² = C₂×He₃⋊₃D₄	φ: C₂²/C₂ → C₂ ⊆ Out C₂×C₃²⋊C₆	72		(C2xC3^2:C6):5C2^2	432,322
(C₂×C₃²⋊C₆)⋊₆C₂² = C₆²⋊D₆	φ: C₂²/C₂ → C₂ ⊆ Out C₂×C₃²⋊C₆	36	12+	(C2xC3^2:C6):6C2^2	432,323
(C₂×C₃²⋊C₆)⋊₇C₂² = C₂×He₃⋊₄D₄	φ: C₂²/C₂ → C₂ ⊆ Out C₂×C₃²⋊C₆	72		(C2xC3^2:C6):7C2^2	432,350
(C₂×C₃²⋊C₆)⋊₈C₂² = D₄×C₃²⋊C₆	φ: C₂²/C₂ → C₂ ⊆ Out C₂×C₃²⋊C₆	36	12+	(C2xC3^2:C6):8C2^2	432,360
(C₂×C₃²⋊C₆)⋊₉C₂² = C₂×He₃⋊₆D₄	φ: C₂²/C₂ → C₂ ⊆ Out C₂×C₃²⋊C₆	72		(C2xC3^2:C6):9C2^2	432,377
(C₂×C₃²⋊C₆)⋊₁₀C₂² = C₂²×C₃²⋊D₆	φ: C₂²/C₂ → C₂ ⊆ Out C₂×C₃²⋊C₆	36		(C2xC3^2:C6):10C2^2	432,545

Non-split extensions G=N.Q with N=C₂×C₃²⋊C₆ and Q=C₂²

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂×C₃²⋊C₆).₁C₂² = C₁₂.₈₄S₃²	φ: C₂²/C₁ → C₂² ⊆ Out C₂×C₃²⋊C₆	72	6	(C2xC3^2:C6).1C2^2	432,296
(C₂×C₃²⋊C₆).₂C₂² = C₆².₈D₆	φ: C₂²/C₁ → C₂² ⊆ Out C₂×C₃²⋊C₆	72	12-	(C2xC3^2:C6).2C2^2	432,318
(C₂×C₃²⋊C₆).₃C₂² = C₆².₉D₆	φ: C₂²/C₁ → C₂² ⊆ Out C₂×C₃²⋊C₆	72	6	(C2xC3^2:C6).3C2^2	432,319
(C₂×C₃²⋊C₆).₄C₂² = C₃⋊S₃⋊Dic₆	φ: C₂²/C₂ → C₂ ⊆ Out C₂×C₃²⋊C₆	72	12-	(C2xC3^2:C6).4C2^2	432,294
(C₂×C₃²⋊C₆).₅C₂² = C₁₂⋊S₃⋊S₃	φ: C₂²/C₂ → C₂ ⊆ Out C₂×C₃²⋊C₆	72	12+	(C2xC3^2:C6).5C2^2	432,295
(C₂×C₃²⋊C₆).₆C₂² = C₁₂.₉₁S₃²	φ: C₂²/C₂ → C₂ ⊆ Out C₂×C₃²⋊C₆	72	6	(C2xC3^2:C6).6C2^2	432,297
(C₂×C₃²⋊C₆).₇C₂² = C₁₂.S₃²	φ: C₂²/C₂ → C₂ ⊆ Out C₂×C₃²⋊C₆	72	12-	(C2xC3^2:C6).7C2^2	432,299
(C₂×C₃²⋊C₆).₈C₂² = C₄×C₃²⋊D₆	φ: C₂²/C₂ → C₂ ⊆ Out C₂×C₃²⋊C₆	36	6	(C2xC3^2:C6).8C2^2	432,300
(C₂×C₃²⋊C₆).₉C₂² = C₂×C₆.S₃²	φ: C₂²/C₂ → C₂ ⊆ Out C₂×C₃²⋊C₆	72		(C2xC3^2:C6).9C2^2	432,317
(C₂×C₃²⋊C₆).₁₀C₂² = C₆².₃₆D₆	φ: C₂²/C₂ → C₂ ⊆ Out C₂×C₃²⋊C₆	72	6	(C2xC3^2:C6).10C2^2	432,351
(C₂×C₃²⋊C₆).₁₁C₂² = C₆².₁₃D₆	φ: C₂²/C₂ → C₂ ⊆ Out C₂×C₃²⋊C₆	72	12-	(C2xC3^2:C6).11C2^2	432,361
(C₂×C₃²⋊C₆).₁₂C₂² = (Q₈×He₃)⋊C₂	φ: C₂²/C₂ → C₂ ⊆ Out C₂×C₃²⋊C₆	72	12+	(C2xC3^2:C6).12C2^2	432,369
(C₂×C₃²⋊C₆).₁₃C₂² = C₂×C₄×C₃²⋊C₆	φ: trivial image	72		(C2xC3^2:C6).13C2^2	432,349
(C₂×C₃²⋊C₆).₁₄C₂² = Q₈×C₃²⋊C₆	φ: trivial image	72	12-	(C2xC3^2:C6).14C2^2	432,368

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