Extensions 1→N→G→Q→1 with N=C₃ and Q=Q₈×C₃²

Direct product G=N×Q with N=C₃ and Q=Q₈×C₃²

		d	ρ	Label	ID
Q₈×C₃³		216		Q8xC3^3	216,152

Semidirect products G=N:Q with N=C₃ and Q=Q₈×C₃²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(Q₈×C₃²) = C₃²×Dic₆	φ: Q₈×C₃²/C₃×C₁₂ → C₂ ⊆ Aut C₃	72		C3:(Q8xC3^2)	216,135

Non-split extensions G=N.Q with N=C₃ and Q=Q₈×C₃²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(Q₈×C₃²) = Q₈×C₃×C₉	central extension (φ=1)	216		C3.1(Q8xC3^2)	216,79
C₃.₂(Q₈×C₃²) = Q₈×He₃	central stem extension (φ=1)	72	6	C3.2(Q8xC3^2)	216,80
C₃.₃(Q₈×C₃²) = Q₈×3_-¹⁺²	central stem extension (φ=1)	72	6	C3.3(Q8xC3^2)	216,81

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Extensions 1→N→G→Q→1 with N=C3 and Q=Q8×C32