Extensions 1→N→G→Q→1 with N=C₃³ and Q=S₃

Direct product G=N×Q with N=C₃³ and Q=S₃

		d	ρ	Label	ID
S₃×C₃³		54		S3xC3^3	162,51

Semidirect products G=N:Q with N=C₃³ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃³⋊₁S₃ = C₃≀S₃	φ: S₃/C₁ → S₃ ⊆ Aut C₃³	9	3	C3^3:1S3	162,10
C₃³⋊₂S₃ = C₃³⋊S₃	φ: S₃/C₁ → S₃ ⊆ Aut C₃³	9	6+	C3^3:2S3	162,19
C₃³⋊₃S₃ = C₃×C₃²⋊C₆	φ: S₃/C₁ → S₃ ⊆ Aut C₃³	18	6	C3^3:3S3	162,34
C₃³⋊₄S₃ = He₃⋊₄S₃	φ: S₃/C₁ → S₃ ⊆ Aut C₃³	27		C3^3:4S3	162,40
C₃³⋊₅S₃ = C₃×He₃⋊C₂	φ: S₃/C₁ → S₃ ⊆ Aut C₃³	27		C3^3:5S3	162,41
C₃³⋊₆S₃ = He₃⋊₅S₃	φ: S₃/C₁ → S₃ ⊆ Aut C₃³	18	6	C3^3:6S3	162,46
C₃³⋊₇S₃ = C₃²×C₃⋊S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₃³	18		C3^3:7S3	162,52
C₃³⋊₈S₃ = C₃×C₃³⋊C₂	φ: S₃/C₃ → C₂ ⊆ Aut C₃³	54		C3^3:8S3	162,53
C₃³⋊₉S₃ = C₃⁴⋊C₂	φ: S₃/C₃ → C₂ ⊆ Aut C₃³	81		C3^3:9S3	162,54

Non-split extensions G=N.Q with N=C₃³ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃³.₁S₃ = C₃²⋊D₉	φ: S₃/C₁ → S₃ ⊆ Aut C₃³	27		C3^3.1S3	162,5
C₃³.₂S₃ = C₃²⋊₂D₉	φ: S₃/C₁ → S₃ ⊆ Aut C₃³	18	6	C3^3.2S3	162,17
C₃³.₃S₃ = C₃×C₉⋊C₆	φ: S₃/C₁ → S₃ ⊆ Aut C₃³	18	6	C3^3.3S3	162,36
C₃³.₄S₃ = C₃³.S₃	φ: S₃/C₁ → S₃ ⊆ Aut C₃³	27		C3^3.4S3	162,42
C₃³.₅S₃ = C₃²×D₉	φ: S₃/C₃ → C₂ ⊆ Aut C₃³	54		C3^3.5S3	162,32
C₃³.₆S₃ = C₃×C₉⋊S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₃³	54		C3^3.6S3	162,38
C₃³.₇S₃ = C₃²⋊₄D₉	φ: S₃/C₃ → C₂ ⊆ Aut C₃³	81		C3^3.7S3	162,45

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