Extensions 1→N→G→Q→1 with N=C₃ and Q=D₄×C₁₂

Direct product G=N×Q with N=C₃ and Q=D₄×C₁₂

		d	ρ	Label	ID
D₄×C₃×C₁₂		144		D4xC3xC12	288,815

Semidirect products G=N:Q with N=C₃ and Q=D₄×C₁₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(D₄×C₁₂) = C₁₂×D₁₂	φ: D₄×C₁₂/C₄×C₁₂ → C₂ ⊆ Aut C₃	96		C3:1(D4xC12)	288,644
C₃⋊₂(D₄×C₁₂) = C₃×Dic₃⋊₄D₄	φ: D₄×C₁₂/C₃×C₂²⋊C₄ → C₂ ⊆ Aut C₃	48		C3:2(D4xC12)	288,652
C₃⋊₃(D₄×C₁₂) = C₃×Dic₃⋊₅D₄	φ: D₄×C₁₂/C₃×C₄⋊C₄ → C₂ ⊆ Aut C₃	96		C3:3(D4xC12)	288,664
C₃⋊₄(D₄×C₁₂) = C₁₂×C₃⋊D₄	φ: D₄×C₁₂/C₂²×C₁₂ → C₂ ⊆ Aut C₃	48		C3:4(D4xC12)	288,699
C₃⋊₅(D₄×C₁₂) = C₃×D₄×Dic₃	φ: D₄×C₁₂/C₆×D₄ → C₂ ⊆ Aut C₃	48		C3:5(D4xC12)	288,705

Non-split extensions G=N.Q with N=C₃ and Q=D₄×C₁₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(D₄×C₁₂) = D₄×C₃₆	central extension (φ=1)	144		C3.(D4xC12)	288,168

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