Extensions 1→N→G→Q→1 with N=C₇₂ and Q=S₃

Direct product G=N×Q with N=C₇₂ and Q=S₃

		d	ρ	Label	ID
S₃×C₇₂		144	2	S3xC72	432,109

Semidirect products G=N:Q with N=C₇₂ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₇₂⋊₁S₃ = C₇₂⋊₁S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₇₂	216		C72:1S3	432,172
C₇₂⋊₂S₃ = C₂₄⋊D₉	φ: S₃/C₃ → C₂ ⊆ Aut C₇₂	216		C72:2S3	432,171
C₇₂⋊₃S₃ = C₈×C₉⋊S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₇₂	216		C72:3S3	432,169
C₇₂⋊₄S₃ = C₇₂⋊S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₇₂	216		C72:4S3	432,170
C₇₂⋊₅S₃ = C₉×D₂₄	φ: S₃/C₃ → C₂ ⊆ Aut C₇₂	144	2	C72:5S3	432,112
C₇₂⋊₆S₃ = C₉×C₂₄⋊C₂	φ: S₃/C₃ → C₂ ⊆ Aut C₇₂	144	2	C72:6S3	432,111
C₇₂⋊₇S₃ = C₉×C₈⋊S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₇₂	144	2	C72:7S3	432,110

Non-split extensions G=N.Q with N=C₇₂ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₇₂.₁S₃ = Dic₁₀₈	φ: S₃/C₃ → C₂ ⊆ Aut C₇₂	432	2-	C72.1S3	432,4
C₇₂.₂S₃ = D₂₁₆	φ: S₃/C₃ → C₂ ⊆ Aut C₇₂	216	2+	C72.2S3	432,8
C₇₂.₃S₃ = C₂₄.D₉	φ: S₃/C₃ → C₂ ⊆ Aut C₇₂	432		C72.3S3	432,168
C₇₂.₄S₃ = C₂₁₆⋊C₂	φ: S₃/C₃ → C₂ ⊆ Aut C₇₂	216	2	C72.4S3	432,7
C₇₂.₅S₃ = C₂₇⋊C₁₆	φ: S₃/C₃ → C₂ ⊆ Aut C₇₂	432	2	C72.5S3	432,1
C₇₂.₆S₃ = C₈×D₂₇	φ: S₃/C₃ → C₂ ⊆ Aut C₇₂	216	2	C72.6S3	432,5
C₇₂.₇S₃ = C₈⋊D₂₇	φ: S₃/C₃ → C₂ ⊆ Aut C₇₂	216	2	C72.7S3	432,6
C₇₂.₈S₃ = C₇₂.S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₇₂	432		C72.8S3	432,32
C₇₂.₉S₃ = C₉×Dic₁₂	φ: S₃/C₃ → C₂ ⊆ Aut C₇₂	144	2	C72.9S3	432,113
C₇₂.₁₀S₃ = C₉×C₃⋊C₁₆	central extension (φ=1)	144	2	C72.10S3	432,29

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