Extensions 1→N→G→Q→1 with N=C₃ and Q=C₂³.₁₂D₆

Direct product G=N×Q with N=C₃ and Q=C₂³.₁₂D₆

		d	ρ	Label	ID
C₃×C₂³.₁₂D₆		48		C3xC2^3.12D6	288,707

Semidirect products G=N:Q with N=C₃ and Q=C₂³.₁₂D₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₂³.₁₂D₆) = C₁₂.₂₇D₁₂	φ: C₂³.₁₂D₆/C₄×Dic₃ → C₂ ⊆ Aut C₃	96		C3:1(C2^3.12D6)	288,508
C₃⋊₂(C₂³.₁₂D₆) = C₆².₁₀₁C₂³	φ: C₂³.₁₂D₆/C₆.D₄ → C₂ ⊆ Aut C₃	48		C3:2(C2^3.12D6)	288,607
C₃⋊₃(C₂³.₁₂D₆) = C₆².₃₃C₂³	φ: C₂³.₁₂D₆/C₂×Dic₆ → C₂ ⊆ Aut C₃	96		C3:3(C2^3.12D6)	288,511
C₃⋊₄(C₂³.₁₂D₆) = C₆².₂₅₄C₂³	φ: C₂³.₁₂D₆/C₆×D₄ → C₂ ⊆ Aut C₃	144		C3:4(C2^3.12D6)	288,793

Non-split extensions G=N.Q with N=C₃ and Q=C₂³.₁₂D₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(C₂³.₁₂D₆) = C₃₆.₁₇D₄	φ: C₂³.₁₂D₆/C₆×D₄ → C₂ ⊆ Aut C₃	144		C3.(C2^3.12D6)	288,146

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