Extensions 1→N→G→Q→1 with N=C₃² and Q=C₄.A₄

Direct product G=N×Q with N=C₃² and Q=C₄.A₄

		d	ρ	Label	ID
C₃²×C₄.A₄		144		C3^2xC4.A4	432,699

Semidirect products G=N:Q with N=C₃² and Q=C₄.A₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃²⋊(C₄.A₄) = C₆.(S₃×A₄)	φ: C₄.A₄/Q₈ → C₆ ⊆ Aut C₃²	72	12+	C3^2:(C4.A4)	432,269
C₃²⋊₂(C₄.A₄) = C₄○D₄⋊He₃	φ: C₄.A₄/C₄○D₄ → C₃ ⊆ Aut C₃²	72	6	C3^2:2(C4.A4)	432,339
C₃²⋊₃(C₄.A₄) = C₃×Dic₃.A₄	φ: C₄.A₄/SL₂(𝔽₃) → C₂ ⊆ Aut C₃²	48	4	C3^2:3(C4.A4)	432,622
C₃²⋊₄(C₄.A₄) = C₃⋊Dic₃.₂A₄	φ: C₄.A₄/SL₂(𝔽₃) → C₂ ⊆ Aut C₃²	144		C3^2:4(C4.A4)	432,625

Non-split extensions G=N.Q with N=C₃² and Q=C₄.A₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃².(C₄.A₄) = Q₈⋊C₉⋊₄C₆	φ: C₄.A₄/C₄○D₄ → C₃ ⊆ Aut C₃²	72	6	C3^2.(C4.A4)	432,338
C₃².₂(C₄.A₄) = Q₈⋊C₉⋊₃S₃	φ: C₄.A₄/SL₂(𝔽₃) → C₂ ⊆ Aut C₃²	144	4	C3^2.2(C4.A4)	432,267
C₃².₃(C₄.A₄) = C₃×Q₈.C₁₈	central extension (φ=1)	216		C3^2.3(C4.A4)	432,337

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