Extensions 1→N→G→Q→1 with N=C₃² and Q=C₂×SL₂(𝔽₃)

Direct product G=N×Q with N=C₃² and Q=C₂×SL₂(𝔽₃)

		d	ρ	Label	ID
C₃×C₆×SL₂(𝔽₃)		144		C3xC6xSL(2,3)	432,698

Semidirect products G=N:Q with N=C₃² and Q=C₂×SL₂(𝔽₃)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃²⋊(C₂×SL₂(𝔽₃)) = C₂×ASL₂(𝔽₃)	φ: C₂×SL₂(𝔽₃)/C₂ → SL₂(𝔽₃) ⊆ Aut C₃²	18	8+	C3^2:(C2xSL(2,3))	432,735
C₃²⋊₂(C₂×SL₂(𝔽₃)) = Q₈⋊He₃⋊C₂	φ: C₂×SL₂(𝔽₃)/Q₈ → C₆ ⊆ Aut C₃²	72	12-	C3^2:2(C2xSL(2,3))	432,270
C₃²⋊₃(C₂×SL₂(𝔽₃)) = C₂×Q₈⋊He₃	φ: C₂×SL₂(𝔽₃)/C₂×Q₈ → C₃ ⊆ Aut C₃²	144		C3^2:3(C2xSL(2,3))	432,336
C₃²⋊₄(C₂×SL₂(𝔽₃)) = C₃×S₃×SL₂(𝔽₃)	φ: C₂×SL₂(𝔽₃)/SL₂(𝔽₃) → C₂ ⊆ Aut C₃²	48	4	C3^2:4(C2xSL(2,3))	432,623
C₃²⋊₅(C₂×SL₂(𝔽₃)) = C₃⋊S₃×SL₂(𝔽₃)	φ: C₂×SL₂(𝔽₃)/SL₂(𝔽₃) → C₂ ⊆ Aut C₃²	72		C3^2:5(C2xSL(2,3))	432,626

Non-split extensions G=N.Q with N=C₃² and Q=C₂×SL₂(𝔽₃)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃².(C₂×SL₂(𝔽₃)) = C₂×Q₈⋊3_-¹⁺²	φ: C₂×SL₂(𝔽₃)/C₂×Q₈ → C₃ ⊆ Aut C₃²	144		C3^2.(C2xSL(2,3))	432,335
C₃².₂(C₂×SL₂(𝔽₃)) = S₃×Q₈⋊C₉	φ: C₂×SL₂(𝔽₃)/SL₂(𝔽₃) → C₂ ⊆ Aut C₃²	144	4	C3^2.2(C2xSL(2,3))	432,268
C₃².₃(C₂×SL₂(𝔽₃)) = C₆×Q₈⋊C₉	central extension (φ=1)	432		C3^2.3(C2xSL(2,3))	432,334

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