Extensions 1→N→G→Q→1 with N=Q₈ and Q=C₃²×C₆

Direct product G=N×Q with N=Q₈ and Q=C₃²×C₆

		d	ρ	Label	ID
Q₈×C₃²×C₆		432		Q8xC3^2xC6	432,732

Semidirect products G=N:Q with N=Q₈ and Q=C₃²×C₆

extension	φ:Q→Out N	d	Label	ID
Q₈⋊(C₃²×C₆) = C₃×C₆×SL₂(𝔽₃)	φ: C₃²×C₆/C₃×C₆ → C₃ ⊆ Out Q₈	144	Q8:(C3^2xC6)	432,698
Q₈⋊₂(C₃²×C₆) = SD₁₆×C₃³	φ: C₃²×C₆/C₃³ → C₂ ⊆ Out Q₈	216	Q8:2(C3^2xC6)	432,518
Q₈⋊₃(C₃²×C₆) = C₄○D₄×C₃³	φ: trivial image	216	Q8:3(C3^2xC6)	432,733

Non-split extensions G=N.Q with N=Q₈ and Q=C₃²×C₆

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈.(C₃²×C₆) = C₃²×C₄.A₄	φ: C₃²×C₆/C₃×C₆ → C₃ ⊆ Out Q₈	144		Q8.(C3^2xC6)	432,699
Q₈.₂(C₃²×C₆) = Q₁₆×C₃³	φ: C₃²×C₆/C₃³ → C₂ ⊆ Out Q₈	432		Q8.2(C3^2xC6)	432,519

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Extensions 1→N→G→Q→1 with N=Q8 and Q=C32×C6