Extensions 1→N→G→Q→1 with N=C₃ and Q=C₂³⋊₂D₆

Direct product G=N×Q with N=C₃ and Q=C₂³⋊₂D₆

		d	ρ	Label	ID
C₃×C₂³⋊₂D₆		48		C3xC2^3:2D6	288,708

Semidirect products G=N:Q with N=C₃ and Q=C₂³⋊₂D₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₂³⋊₂D₆) = D₆⋊₄D₁₂	φ: C₂³⋊₂D₆/D₆⋊C₄ → C₂ ⊆ Aut C₃	48		C3:1(C2^3:2D6)	288,570
C₃⋊₂(C₂³⋊₂D₆) = C₆²⋊₈D₄	φ: C₂³⋊₂D₆/C₆.D₄ → C₂ ⊆ Aut C₃	24		C3:2(C2^3:2D6)	288,629
C₃⋊₃(C₂³⋊₂D₆) = C₆².₁₂₅C₂³	φ: C₂³⋊₂D₆/C₂×C₃⋊D₄ → C₂ ⊆ Aut C₃	48		C3:3(C2^3:2D6)	288,631
C₃⋊₄(C₂³⋊₂D₆) = C₆²⋊₁₃D₄	φ: C₂³⋊₂D₆/C₆×D₄ → C₂ ⊆ Aut C₃	72		C3:4(C2^3:2D6)	288,794
C₃⋊₅(C₂³⋊₂D₆) = C₆²⋊₄D₄	φ: C₂³⋊₂D₆/S₃×C₂³ → C₂ ⊆ Aut C₃	48		C3:5(C2^3:2D6)	288,624

Non-split extensions G=N.Q with N=C₃ and Q=C₂³⋊₂D₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(C₂³⋊₂D₆) = C₂³⋊₂D₁₈	φ: C₂³⋊₂D₆/C₆×D₄ → C₂ ⊆ Aut C₃	72		C3.(C2^3:2D6)	288,147

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