Extensions 1→N→G→Q→1 with N=Q₈ and Q=C₃²⋊C₆

Direct product G=N×Q with N=Q₈ and Q=C₃²⋊C₆

		d	ρ	Label	ID
Q₈×C₃²⋊C₆		72	12-	Q8xC3^2:C6	432,368

Semidirect products G=N:Q with N=Q₈ and Q=C₃²⋊C₆

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈⋊(C₃²⋊C₆) = C₃²⋊₂GL₂(𝔽₃)	φ: C₃²⋊C₆/C₃² → S₃ ⊆ Out Q₈	72	12+	Q8:(C3^2:C6)	432,248
Q₈⋊₂(C₃²⋊C₆) = Q₈⋊He₃⋊C₂	φ: C₃²⋊C₆/C₃⋊S₃ → C₃ ⊆ Out Q₈	72	12-	Q8:2(C3^2:C6)	432,270
Q₈⋊₃(C₃²⋊C₆) = He₃⋊₁₀SD₁₆	φ: C₃²⋊C₆/He₃ → C₂ ⊆ Out Q₈	72	12+	Q8:3(C3^2:C6)	432,161
Q₈⋊₄(C₃²⋊C₆) = (Q₈×He₃)⋊C₂	φ: trivial image	72	12+	Q8:4(C3^2:C6)	432,369

Non-split extensions G=N.Q with N=Q₈ and Q=C₃²⋊C₆

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈.(C₃²⋊C₆) = C₃²⋊CSU₂(𝔽₃)	φ: C₃²⋊C₆/C₃² → S₃ ⊆ Out Q₈	144	12-	Q8.(C3^2:C6)	432,247
Q₈.₂(C₃²⋊C₆) = C₆.(S₃×A₄)	φ: C₃²⋊C₆/C₃⋊S₃ → C₃ ⊆ Out Q₈	72	12+	Q8.2(C3^2:C6)	432,269
Q₈.₃(C₃²⋊C₆) = He₃⋊₆Q₁₆	φ: C₃²⋊C₆/He₃ → C₂ ⊆ Out Q₈	144	12-	Q8.3(C3^2:C6)	432,160

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