Extensions 1→N→G→Q→1 with N=C₆₈ and Q=S₃

Direct product G=N×Q with N=C₆₈ and Q=S₃

		d	ρ	Label	ID
S₃×C₆₈		204	2	S3xC68	408,21

Semidirect products G=N:Q with N=C₆₈ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆₈⋊₁S₃ = D₂₀₄	φ: S₃/C₃ → C₂ ⊆ Aut C₆₈	204	2+	C68:1S3	408,27
C₆₈⋊₂S₃ = C₄×D₅₁	φ: S₃/C₃ → C₂ ⊆ Aut C₆₈	204	2	C68:2S3	408,26
C₆₈⋊₃S₃ = C₁₇×D₁₂	φ: S₃/C₃ → C₂ ⊆ Aut C₆₈	204	2	C68:3S3	408,22

Non-split extensions G=N.Q with N=C₆₈ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆₈.₁S₃ = Dic₁₀₂	φ: S₃/C₃ → C₂ ⊆ Aut C₆₈	408	2-	C68.1S3	408,25
C₆₈.₂S₃ = C₅₁⋊₅C₈	φ: S₃/C₃ → C₂ ⊆ Aut C₆₈	408	2	C68.2S3	408,3
C₆₈.₃S₃ = C₁₇×Dic₆	φ: S₃/C₃ → C₂ ⊆ Aut C₆₈	408	2	C68.3S3	408,20
C₆₈.₄S₃ = C₁₇×C₃⋊C₈	central extension (φ=1)	408	2	C68.4S3	408,1

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