Extensions 1→N→G→Q→1 with N=C₂³ and Q=SL₂(𝔽₃)

Direct product G=N×Q with N=C₂³ and Q=SL₂(𝔽₃)

		d	ρ	Label	ID
C₂³×SL₂(𝔽₃)		64		C2^3xSL(2,3)	192,1498

Semidirect products G=N:Q with N=C₂³ and Q=SL₂(𝔽₃)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊₁SL₂(𝔽₃) = C₂⁴.A₄	φ: SL₂(𝔽₃)/C₂ → A₄ ⊆ Aut C₂³	24	6	C2^3:1SL(2,3)	192,195
C₂³⋊₂SL₂(𝔽₃) = C₂⁴.₇A₄	φ: SL₂(𝔽₃)/C₂ → A₄ ⊆ Aut C₂³	16		C2^3:2SL(2,3)	192,1021
C₂³⋊₃SL₂(𝔽₃) = C₂×Q₈⋊A₄	φ: SL₂(𝔽₃)/Q₈ → C₃ ⊆ Aut C₂³	48		C2^3:3SL(2,3)	192,1506

Non-split extensions G=N.Q with N=C₂³ and Q=SL₂(𝔽₃)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.₁SL₂(𝔽₃) = C₂³.SL₂(𝔽₃)	φ: SL₂(𝔽₃)/C₂ → A₄ ⊆ Aut C₂³	16	4	C2^3.1SL(2,3)	192,4
C₂³.₂SL₂(𝔽₃) = C₂⁴.₂A₄	φ: SL₂(𝔽₃)/C₂ → A₄ ⊆ Aut C₂³	12	6+	C2^3.2SL(2,3)	192,197
C₂³.₃SL₂(𝔽₃) = C₂⁴.₃A₄	φ: SL₂(𝔽₃)/C₂ → A₄ ⊆ Aut C₂³	24	6	C2^3.3SL(2,3)	192,198
C₂³.₄SL₂(𝔽₃) = C₂×C₂³.₃A₄	φ: SL₂(𝔽₃)/Q₈ → C₃ ⊆ Aut C₂³	24		C2^3.4SL(2,3)	192,189

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