Extensions 1→N→G→Q→1 with N=C₂³ and Q=C₉⋊S₃

Direct product G=N×Q with N=C₂³ and Q=C₉⋊S₃

		d	ρ	Label	ID
C₂³×C₉⋊S₃		216		C2^3xC9:S3	432,560

Semidirect products G=N:Q with N=C₂³ and Q=C₉⋊S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊₁(C₉⋊S₃) = C₂×C₉⋊S₄	φ: C₉⋊S₃/C₉ → S₃ ⊆ Aut C₂³	54	6+	C2^3:1(C9:S3)	432,536
C₂³⋊₂(C₉⋊S₃) = C₂×C₃².₃S₄	φ: C₉⋊S₃/C₃² → S₃ ⊆ Aut C₂³	54		C2^3:2(C9:S3)	432,537
C₂³⋊₃(C₉⋊S₃) = C₂×C₆.D₁₈	φ: C₉⋊S₃/C₃×C₉ → C₂ ⊆ Aut C₂³	216		C2^3:3(C9:S3)	432,397

Non-split extensions G=N.Q with N=C₂³ and Q=C₉⋊S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.₁(C₉⋊S₃) = A₄⋊Dic₉	φ: C₉⋊S₃/C₉ → S₃ ⊆ Aut C₂³	108	6-	C2^3.1(C9:S3)	432,254
C₂³.₂(C₉⋊S₃) = C₆².₁₀Dic₃	φ: C₉⋊S₃/C₃² → S₃ ⊆ Aut C₂³	108		C2^3.2(C9:S3)	432,259
C₂³.₃(C₉⋊S₃) = C₆².₁₂₇D₆	φ: C₉⋊S₃/C₃×C₉ → C₂ ⊆ Aut C₂³	216		C2^3.3(C9:S3)	432,198
C₂³.₄(C₉⋊S₃) = C₂²×C₉⋊Dic₃	central extension (φ=1)	432		C2^3.4(C9:S3)	432,396

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