Extensions 1→N→G→Q→1 with N=C₃ and Q=C₃×C₄.₄D₄

Direct product G=N×Q with N=C₃ and Q=C₃×C₄.₄D₄

		d	ρ	Label	ID
C₃²×C₄.₄D₄		144		C3^2xC4.4D4	288,821

Semidirect products G=N:Q with N=C₃ and Q=C₃×C₄.₄D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₃×C₄.₄D₄) = C₃×C₄²⋊₇S₃	φ: C₃×C₄.₄D₄/C₄×C₁₂ → C₂ ⊆ Aut C₃	96		C3:1(C3xC4.4D4)	288,646
C₃⋊₂(C₃×C₄.₄D₄) = C₃×C₂³.₁₁D₆	φ: C₃×C₄.₄D₄/C₃×C₂²⋊C₄ → C₂ ⊆ Aut C₃	48		C3:2(C3xC4.4D4)	288,656
C₃⋊₃(C₃×C₄.₄D₄) = C₃×C₂³.₁₂D₆	φ: C₃×C₄.₄D₄/C₆×D₄ → C₂ ⊆ Aut C₃	48		C3:3(C3xC4.4D4)	288,707
C₃⋊₄(C₃×C₄.₄D₄) = C₃×C₁₂.₂₃D₄	φ: C₃×C₄.₄D₄/C₆×Q₈ → C₂ ⊆ Aut C₃	96		C3:4(C3xC4.4D4)	288,718

Non-split extensions G=N.Q with N=C₃ and Q=C₃×C₄.₄D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(C₃×C₄.₄D₄) = C₉×C₄.₄D₄	central extension (φ=1)	144		C3.(C3xC4.4D4)	288,174

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