Extensions 1→N→G→Q→1 with N=C₃ and Q=Q₈×C₃×C₆

Direct product G=N×Q with N=C₃ and Q=Q₈×C₃×C₆

		d	ρ	Label	ID
Q₈×C₃²×C₆		432		Q8xC3^2xC6	432,732

Semidirect products G=N:Q with N=C₃ and Q=Q₈×C₃×C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(Q₈×C₃×C₆) = C₃×C₆×Dic₆	φ: Q₈×C₃×C₆/C₆×C₁₂ → C₂ ⊆ Aut C₃	144		C3:1(Q8xC3xC6)	432,700
C₃⋊₂(Q₈×C₃×C₆) = S₃×Q₈×C₃²	φ: Q₈×C₃×C₆/Q₈×C₃² → C₂ ⊆ Aut C₃	144		C3:2(Q8xC3xC6)	432,706

Non-split extensions G=N.Q with N=C₃ and Q=Q₈×C₃×C₆

extension	φ:Q→Aut N	d	Label	ID
C₃.₁(Q₈×C₃×C₆) = Q₈×C₃×C₁₈	central extension (φ=1)	432	C3.1(Q8xC3xC6)	432,406
C₃.₂(Q₈×C₃×C₆) = C₂×Q₈×He₃	central stem extension (φ=1)	144	C3.2(Q8xC3xC6)	432,407
C₃.₃(Q₈×C₃×C₆) = C₂×Q₈×3_-¹⁺²	central stem extension (φ=1)	144	C3.3(Q8xC3xC6)	432,408

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Extensions 1→N→G→Q→1 with N=C3 and Q=Q8×C3×C6