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

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

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

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃²⋊(C₃×Q₈) = C₃×PSU₃(𝔽₂)	φ: C₃×Q₈/C₃ → Q₈ ⊆ Aut C₃²	24	8	C3^2:(C3xQ8)	216,160
C₃²⋊₂(C₃×Q₈) = He₃⋊₃Q₈	φ: C₃×Q₈/C₄ → C₆ ⊆ Aut C₃²	72	6-	C3^2:2(C3xQ8)	216,49
C₃²⋊₃(C₃×Q₈) = C₃×C₃²⋊₂Q₈	φ: C₃×Q₈/C₆ → C₂² ⊆ Aut C₃²	24	4	C3^2:3(C3xQ8)	216,123
C₃²⋊₄(C₃×Q₈) = Q₈×He₃	φ: C₃×Q₈/Q₈ → C₃ ⊆ Aut C₃²	72	6	C3^2:4(C3xQ8)	216,80
C₃²⋊₅(C₃×Q₈) = C₃²×Dic₆	φ: C₃×Q₈/C₁₂ → C₂ ⊆ Aut C₃²	72		C3^2:5(C3xQ8)	216,135
C₃²⋊₆(C₃×Q₈) = C₃×C₃²⋊₄Q₈	φ: C₃×Q₈/C₁₂ → C₂ ⊆ Aut C₃²	72		C3^2:6(C3xQ8)	216,140

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃².(C₃×Q₈) = Q₈×3_-¹⁺²	φ: C₃×Q₈/Q₈ → C₃ ⊆ Aut C₃²	72	6	C3^2.(C3xQ8)	216,81
C₃².₂(C₃×Q₈) = C₉×Dic₆	φ: C₃×Q₈/C₁₂ → C₂ ⊆ Aut C₃²	72	2	C3^2.2(C3xQ8)	216,44
C₃².₃(C₃×Q₈) = Q₈×C₃×C₉	central extension (φ=1)	216		C3^2.3(C3xQ8)	216,79

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