Extensions 1→N→G→Q→1 with N=C₂³×C₆ and Q=C₃²

Direct product G=N×Q with N=C₂³×C₆ and Q=C₃²

		d	ρ	Label	ID
C₂×C₆³		432		C2xC6^3	432,775

Semidirect products G=N:Q with N=C₂³×C₆ and Q=C₃²

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂³×C₆)⋊C₃² = C₃×A₄²	φ: C₃²/C₁ → C₃² ⊆ Aut C₂³×C₆	36	9	(C2^3xC6):C3^2	432,750
(C₂³×C₆)⋊₂C₃² = A₄×C₆²	φ: C₃²/C₃ → C₃ ⊆ Aut C₂³×C₆	108		(C2^3xC6):2C3^2	432,770
(C₂³×C₆)⋊₃C₃² = C₃²×C₂²⋊A₄	φ: C₃²/C₃ → C₃ ⊆ Aut C₂³×C₆	108		(C2^3xC6):3C3^2	432,771

Non-split extensions G=N.Q with N=C₂³×C₆ and Q=C₃²

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂³×C₆).₁C₃² = A₄×C₃.A₄	φ: C₃²/C₁ → C₃² ⊆ Aut C₂³×C₆	54	9	(C2^3xC6).1C3^2	432,524
(C₂³×C₆).₂C₃² = C₃.A₄²	φ: C₃²/C₁ → C₃² ⊆ Aut C₂³×C₆	36	9	(C2^3xC6).2C3^2	432,525
(C₂³×C₆).₃C₃² = C₂⁴⋊He₃	φ: C₃²/C₁ → C₃² ⊆ Aut C₂³×C₆	36	9	(C2^3xC6).3C3^2	432,526
(C₂³×C₆).₄C₃² = C₂⁴⋊3_-¹⁺²	φ: C₃²/C₁ → C₃² ⊆ Aut C₂³×C₆	54	9	(C2^3xC6).4C3^2	432,527
(C₂³×C₆).₅C₃² = C₂⁴⋊₂3_-¹⁺²	φ: C₃²/C₁ → C₃² ⊆ Aut C₂³×C₆	36	9	(C2^3xC6).5C3^2	432,528
(C₂³×C₆).₆C₃² = A₄×C₂×C₁₈	φ: C₃²/C₃ → C₃ ⊆ Aut C₂³×C₆	108		(C2^3xC6).6C3^2	432,546
(C₂³×C₆).₇C₃² = C₂²×C₉⋊A₄	φ: C₃²/C₃ → C₃ ⊆ Aut C₂³×C₆	108		(C2^3xC6).7C3^2	432,547
(C₂³×C₆).₈C₃² = C₂×C₆×C₃.A₄	φ: C₃²/C₃ → C₃ ⊆ Aut C₂³×C₆	108		(C2^3xC6).8C3^2	432,548
(C₂³×C₆).₉C₃² = C₂²×C₃².A₄	φ: C₃²/C₃ → C₃ ⊆ Aut C₂³×C₆	36		(C2^3xC6).9C3^2	432,549
(C₂³×C₆).₁₀C₃² = C₂²×C₃²⋊A₄	φ: C₃²/C₃ → C₃ ⊆ Aut C₂³×C₆	36		(C2^3xC6).10C3^2	432,550
(C₂³×C₆).₁₁C₃² = C₉×C₂²⋊A₄	φ: C₃²/C₃ → C₃ ⊆ Aut C₂³×C₆	108		(C2^3xC6).11C3^2	432,551
(C₂³×C₆).₁₂C₃² = C₂⁴⋊₄3_-¹⁺²	φ: C₃²/C₃ → C₃ ⊆ Aut C₂³×C₆	108		(C2^3xC6).12C3^2	432,552
(C₂³×C₆).₁₃C₃² = C₃×C₂⁴⋊C₉	φ: C₃²/C₃ → C₃ ⊆ Aut C₂³×C₆	108		(C2^3xC6).13C3^2	432,553
(C₂³×C₆).₁₄C₃² = C₆².A₄	φ: C₃²/C₃ → C₃ ⊆ Aut C₂³×C₆	36		(C2^3xC6).14C3^2	432,554
(C₂³×C₆).₁₅C₃² = C₆²⋊A₄	φ: C₃²/C₃ → C₃ ⊆ Aut C₂³×C₆	36		(C2^3xC6).15C3^2	432,555
(C₂³×C₆).₁₆C₃² = C₂⁴×He₃	central extension (φ=1)	144		(C2^3xC6).16C3^2	432,563
(C₂³×C₆).₁₇C₃² = C₂⁴×3_-¹⁺²	central extension (φ=1)	144		(C2^3xC6).17C3^2	432,564

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