Extensions 1→N→G→Q→1 with N=C₂²×C₆² and Q=C₃

Direct product G=N×Q with N=C₂²×C₆² and Q=C₃

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

Semidirect products G=N:Q with N=C₂²×C₆² and Q=C₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂²×C₆²)⋊₁C₃ = C₂²×C₃²⋊A₄	φ: C₃/C₁ → C₃ ⊆ Aut C₂²×C₆²	36		(C2^2xC6^2):1C3	432,550
(C₂²×C₆²)⋊₂C₃ = C₆²⋊A₄	φ: C₃/C₁ → C₃ ⊆ Aut C₂²×C₆²	36		(C2^2xC6^2):2C3	432,555
(C₂²×C₆²)⋊₃C₃ = C₂⁴×He₃	φ: C₃/C₁ → C₃ ⊆ Aut C₂²×C₆²	144		(C2^2xC6^2):3C3	432,563
(C₂²×C₆²)⋊₄C₃ = A₄×C₆²	φ: C₃/C₁ → C₃ ⊆ Aut C₂²×C₆²	108		(C2^2xC6^2):4C3	432,770
(C₂²×C₆²)⋊₅C₃ = C₃²×C₂²⋊A₄	φ: C₃/C₁ → C₃ ⊆ Aut C₂²×C₆²	108		(C2^2xC6^2):5C3	432,771

Non-split extensions G=N.Q with N=C₂²×C₆² and Q=C₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂²×C₆²).₁C₃ = C₂×C₆×C₃.A₄	φ: C₃/C₁ → C₃ ⊆ Aut C₂²×C₆²	108		(C2^2xC6^2).1C3	432,548
(C₂²×C₆²).₂C₃ = C₂²×C₃².A₄	φ: C₃/C₁ → C₃ ⊆ Aut C₂²×C₆²	36		(C2^2xC6^2).2C3	432,549
(C₂²×C₆²).₃C₃ = C₃×C₂⁴⋊C₉	φ: C₃/C₁ → C₃ ⊆ Aut C₂²×C₆²	108		(C2^2xC6^2).3C3	432,553
(C₂²×C₆²).₄C₃ = C₆².A₄	φ: C₃/C₁ → C₃ ⊆ Aut C₂²×C₆²	36		(C2^2xC6^2).4C3	432,554
(C₂²×C₆²).₅C₃ = C₂⁴×3_-¹⁺²	φ: C₃/C₁ → C₃ ⊆ Aut C₂²×C₆²	144		(C2^2xC6^2).5C3	432,564

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁