Extensions 1→N→G→Q→1 with N=C₇₆ and Q=S₃

Direct product G=N×Q with N=C₇₆ and Q=S₃

		d	ρ	Label	ID
S₃×C₇₆		228	2	S3xC76	456,30

Semidirect products G=N:Q with N=C₇₆ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₇₆⋊₁S₃ = D₂₂₈	φ: S₃/C₃ → C₂ ⊆ Aut C₇₆	228	2+	C76:1S3	456,36
C₇₆⋊₂S₃ = C₄×D₅₇	φ: S₃/C₃ → C₂ ⊆ Aut C₇₆	228	2	C76:2S3	456,35
C₇₆⋊₃S₃ = C₁₉×D₁₂	φ: S₃/C₃ → C₂ ⊆ Aut C₇₆	228	2	C76:3S3	456,31

Non-split extensions G=N.Q with N=C₇₆ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₇₆.₁S₃ = Dic₁₁₄	φ: S₃/C₃ → C₂ ⊆ Aut C₇₆	456	2-	C76.1S3	456,34
C₇₆.₂S₃ = C₅₇⋊C₈	φ: S₃/C₃ → C₂ ⊆ Aut C₇₆	456	2	C76.2S3	456,5
C₇₆.₃S₃ = C₁₉×Dic₆	φ: S₃/C₃ → C₂ ⊆ Aut C₇₆	456	2	C76.3S3	456,29
C₇₆.₄S₃ = C₁₉×C₃⋊C₈	central extension (φ=1)	456	2	C76.4S3	456,3

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