Extensions 1→N→G→Q→1 with N=C₃ and Q=D₄×C₂×C₆

Direct product G=N×Q with N=C₃ and Q=D₄×C₂×C₆

		d	ρ	Label	ID
D₄×C₆²		144		D4xC6^2	288,1019

Semidirect products G=N:Q with N=C₃ and Q=D₄×C₂×C₆

extension	φ:Q→Aut N	d	Label	ID
C₃⋊₁(D₄×C₂×C₆) = C₂×C₆×D₁₂	φ: D₄×C₂×C₆/C₂²×C₁₂ → C₂ ⊆ Aut C₃	96	C3:1(D4xC2xC6)	288,990
C₃⋊₂(D₄×C₂×C₆) = S₃×C₆×D₄	φ: D₄×C₂×C₆/C₆×D₄ → C₂ ⊆ Aut C₃	48	C3:2(D4xC2xC6)	288,992
C₃⋊₃(D₄×C₂×C₆) = C₂×C₆×C₃⋊D₄	φ: D₄×C₂×C₆/C₂³×C₆ → C₂ ⊆ Aut C₃	48	C3:3(D4xC2xC6)	288,1002

Non-split extensions G=N.Q with N=C₃ and Q=D₄×C₂×C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(D₄×C₂×C₆) = D₄×C₂×C₁₈	central extension (φ=1)	144		C3.(D4xC2xC6)	288,368

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Extensions 1→N→G→Q→1 with N=C3 and Q=D4×C2×C6