Extensions 1→N→G→Q→1 with N=SL₂(𝔽₃) and Q=Q₈

Direct product G=N×Q with N=SL₂(𝔽₃) and Q=Q₈

		d	ρ	Label	ID
Q₈×SL₂(𝔽₃)		64		Q8xSL(2,3)	192,1007

Semidirect products G=N:Q with N=SL₂(𝔽₃) and Q=Q₈

extension	φ:Q→Out N	d	Label	ID
SL₂(𝔽₃)⋊₁Q₈ = Q₈⋊Dic₆	φ: Q₈/C₄ → C₂ ⊆ Out SL₂(𝔽₃)	64	SL(2,3):1Q8	192,945
SL₂(𝔽₃)⋊₂Q₈ = SL₂(𝔽₃)⋊Q₈	φ: Q₈/C₄ → C₂ ⊆ Out SL₂(𝔽₃)	64	SL(2,3):2Q8	192,950
SL₂(𝔽₃)⋊₃Q₈ = SL₂(𝔽₃)⋊₃Q₈	φ: trivial image	64	SL(2,3):3Q8	192,1006

Non-split extensions G=N.Q with N=SL₂(𝔽₃) and Q=Q₈

extension	φ:Q→Out N	d	ρ	Label	ID
SL₂(𝔽₃).Q₈ = Q₈.Dic₆	φ: Q₈/C₄ → C₂ ⊆ Out SL₂(𝔽₃)	64		SL(2,3).Q8	192,948

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Extensions 1→N→G→Q→1 with N=SL2(𝔽3) and Q=Q8