Extensions 1→N→G→Q→1 with N=C₃ and Q=C₂×GL₂(𝔽₃)

Direct product G=N×Q with N=C₃ and Q=C₂×GL₂(𝔽₃)

		d	ρ	Label	ID
C₆×GL₂(𝔽₃)		48		C6xGL(2,3)	288,900

Semidirect products G=N:Q with N=C₃ and Q=C₂×GL₂(𝔽₃)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₂×GL₂(𝔽₃)) = S₃×GL₂(𝔽₃)	φ: C₂×GL₂(𝔽₃)/GL₂(𝔽₃) → C₂ ⊆ Aut C₃	24	4	C3:1(C2xGL(2,3))	288,851
C₃⋊₂(C₂×GL₂(𝔽₃)) = C₂×C₆.₆S₄	φ: C₂×GL₂(𝔽₃)/C₂×SL₂(𝔽₃) → C₂ ⊆ Aut C₃	48		C3:2(C2xGL(2,3))	288,911

Non-split extensions G=N.Q with N=C₃ and Q=C₂×GL₂(𝔽₃)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(C₂×GL₂(𝔽₃)) = C₂×Q₈⋊D₉	φ: C₂×GL₂(𝔽₃)/C₂×SL₂(𝔽₃) → C₂ ⊆ Aut C₃	144		C3.(C2xGL(2,3))	288,336

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Extensions 1→N→G→Q→1 with N=C3 and Q=C2×GL2(𝔽3)