Extensions 1→N→G→Q→1 with N=C₆₆ and Q=S₃

Direct product G=N×Q with N=C₆₆ and Q=S₃

		d	ρ	Label	ID
S₃×C₆₆		132	2	S3xC66	396,26

Semidirect products G=N:Q with N=C₆₆ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆₆⋊₁S₃ = C₂×C₃⋊D₃₃	φ: S₃/C₃ → C₂ ⊆ Aut C₆₆	198		C66:1S3	396,29
C₆₆⋊₂S₃ = C₆×D₃₃	φ: S₃/C₃ → C₂ ⊆ Aut C₆₆	132	2	C66:2S3	396,27
C₆₆⋊₃S₃ = C₃⋊S₃×C₂₂	φ: S₃/C₃ → C₂ ⊆ Aut C₆₆	198		C66:3S3	396,28

Non-split extensions G=N.Q with N=C₆₆ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆₆.₁S₃ = Dic₉₉	φ: S₃/C₃ → C₂ ⊆ Aut C₆₆	396	2-	C66.1S3	396,3
C₆₆.₂S₃ = D₁₉₈	φ: S₃/C₃ → C₂ ⊆ Aut C₆₆	198	2+	C66.2S3	396,9
C₆₆.₃S₃ = C₃⋊Dic₃₃	φ: S₃/C₃ → C₂ ⊆ Aut C₆₆	396		C66.3S3	396,15
C₆₆.₄S₃ = C₃×Dic₃₃	φ: S₃/C₃ → C₂ ⊆ Aut C₆₆	132	2	C66.4S3	396,13
C₆₆.₅S₃ = C₁₁×Dic₉	φ: S₃/C₃ → C₂ ⊆ Aut C₆₆	396	2	C66.5S3	396,1
C₆₆.₆S₃ = D₉×C₂₂	φ: S₃/C₃ → C₂ ⊆ Aut C₆₆	198	2	C66.6S3	396,8
C₆₆.₇S₃ = C₁₁×C₃⋊Dic₃	φ: S₃/C₃ → C₂ ⊆ Aut C₆₆	396		C66.7S3	396,14
C₆₆.₈S₃ = Dic₃×C₃₃	central extension (φ=1)	132	2	C66.8S3	396,12

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