Extensions 1→N→G→Q→1 with N=C₃ and Q=C₃×C₄²⋊C₂

Direct product G=N×Q with N=C₃ and Q=C₃×C₄²⋊C₂

		d	ρ	Label	ID
C₃²×C₄²⋊C₂		144		C3^2xC4^2:C2	288,814

Semidirect products G=N:Q with N=C₃ and Q=C₃×C₄²⋊C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₃×C₄²⋊C₂) = C₃×C₄²⋊₂S₃	φ: C₃×C₄²⋊C₂/C₄×C₁₂ → C₂ ⊆ Aut C₃	96		C3:1(C3xC4^2:C2)	288,643
C₃⋊₂(C₃×C₄²⋊C₂) = C₃×C₂³.₁₆D₆	φ: C₃×C₄²⋊C₂/C₃×C₂²⋊C₄ → C₂ ⊆ Aut C₃	48		C3:2(C3xC4^2:C2)	288,648
C₃⋊₃(C₃×C₄²⋊C₂) = C₃×C₄⋊C₄⋊₇S₃	φ: C₃×C₄²⋊C₂/C₃×C₄⋊C₄ → C₂ ⊆ Aut C₃	96		C3:3(C3xC4^2:C2)	288,663
C₃⋊₄(C₃×C₄²⋊C₂) = C₃×C₂³.₂₆D₆	φ: C₃×C₄²⋊C₂/C₂²×C₁₂ → C₂ ⊆ Aut C₃	48		C3:4(C3xC4^2:C2)	288,697

Non-split extensions G=N.Q with N=C₃ and Q=C₃×C₄²⋊C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(C₃×C₄²⋊C₂) = C₉×C₄²⋊C₂	central extension (φ=1)	144		C3.(C3xC4^2:C2)	288,167

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