Extensions 1→N→G→Q→1 with N=Q₈×C₂×C₆ and Q=C₃

Direct product G=N×Q with N=Q₈×C₂×C₆ and Q=C₃

		d	ρ	Label	ID
Q₈×C₆²		288		Q8xC6^2	288,1020

Semidirect products G=N:Q with N=Q₈×C₂×C₆ and Q=C₃

extension	φ:Q→Out N	d	ρ	Label	ID
(Q₈×C₂×C₆)⋊₁C₃ = C₂×C₆×SL₂(𝔽₃)	φ: C₃/C₁ → C₃ ⊆ Out Q₈×C₂×C₆	96		(Q8xC2xC6):1C3	288,981
(Q₈×C₂×C₆)⋊₂C₃ = C₃×Q₈×A₄	φ: C₃/C₁ → C₃ ⊆ Out Q₈×C₂×C₆	72	6	(Q8xC2xC6):2C3	288,982
(Q₈×C₂×C₆)⋊₃C₃ = C₃×Q₈⋊A₄	φ: C₃/C₁ → C₃ ⊆ Out Q₈×C₂×C₆	72	6	(Q8xC2xC6):3C3	288,986

Non-split extensions G=N.Q with N=Q₈×C₂×C₆ and Q=C₃

extension	φ:Q→Out N	d	ρ	Label	ID
(Q₈×C₂×C₆).₁C₃ = C₂²×Q₈⋊C₉	φ: C₃/C₁ → C₃ ⊆ Out Q₈×C₂×C₆	288		(Q8xC2xC6).1C3	288,345
(Q₈×C₂×C₆).₂C₃ = Q₈×C₃.A₄	φ: C₃/C₁ → C₃ ⊆ Out Q₈×C₂×C₆	72	6	(Q8xC2xC6).2C3	288,346
(Q₈×C₂×C₆).₃C₃ = C₂²⋊(Q₈⋊C₉)	φ: C₃/C₁ → C₃ ⊆ Out Q₈×C₂×C₆	72	6	(Q8xC2xC6).3C3	288,350
(Q₈×C₂×C₆).₄C₃ = Q₈×C₂×C₁₈	φ: trivial image	288		(Q8xC2xC6).4C3	288,369

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁