Extensions 1→N→G→Q→1 with N=C₃ and Q=C₁₂.₂₆D₆

Direct product G=N×Q with N=C₃ and Q=C₁₂.₂₆D₆

		d	ρ	Label	ID
C₃×C₁₂.₂₆D₆		144		C3xC12.26D6	432,717

Semidirect products G=N:Q with N=C₃ and Q=C₁₂.₂₆D₆

extension	φ:Q→Aut N	d	Label	ID
C₃⋊₁(C₁₂.₂₆D₆) = C₁₂.₄₀S₃²	φ: C₁₂.₂₆D₆/C₄×C₃⋊S₃ → C₂ ⊆ Aut C₃	72	C3:1(C12.26D6)	432,665
C₃⋊₂(C₁₂.₂₆D₆) = C₁₂.₃₉S₃²	φ: C₁₂.₂₆D₆/C₁₂⋊S₃ → C₂ ⊆ Aut C₃	72	C3:2(C12.26D6)	432,664
C₃⋊₃(C₁₂.₂₆D₆) = (Q₈×C₃³)⋊C₂	φ: C₁₂.₂₆D₆/Q₈×C₃² → C₂ ⊆ Aut C₃	216	C3:3(C12.26D6)	432,727

Non-split extensions G=N.Q with N=C₃ and Q=C₁₂.₂₆D₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(C₁₂.₂₆D₆) = C₃₆.₂₉D₆	φ: C₁₂.₂₆D₆/Q₈×C₃² → C₂ ⊆ Aut C₃	216		C3.(C12.26D6)	432,393
C₃.₂(C₁₂.₂₆D₆) = He₃⋊₅D₄⋊C₂	central stem extension (φ=1)	72	6	C3.2(C12.26D6)	432,395

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Extensions 1→N→G→Q→1 with N=C3 and Q=C12.26D6