Extensions 1→N→G→Q→1 with N=He₃⋊₅S₃ and Q=C₃

Direct product G=N×Q with N=He₃⋊₅S₃ and Q=C₃

		d	ρ	Label	ID
C₃×He₃⋊₅S₃		54		C3xHe3:5S3	486,243

Semidirect products G=N:Q with N=He₃⋊₅S₃ and Q=C₃

extension	φ:Q→Out N	d	ρ	Label	ID
He₃⋊₅S₃⋊₁C₃ = C₃.C₃≀S₃	φ: C₃/C₁ → C₃ ⊆ Out He₃⋊₅S₃	54	6	He3:5S3:1C3	486,4
He₃⋊₅S₃⋊₂C₃ = C₃⁴⋊₃S₃	φ: C₃/C₁ → C₃ ⊆ Out He₃⋊₅S₃	18	6	He3:5S3:2C3	486,145
He₃⋊₅S₃⋊₃C₃ = C₃⁴⋊₅S₃	φ: C₃/C₁ → C₃ ⊆ Out He₃⋊₅S₃	18	6	He3:5S3:3C3	486,166
He₃⋊₅S₃⋊₄C₃ = He₃⋊C₃⋊₂S₃	φ: C₃/C₁ → C₃ ⊆ Out He₃⋊₅S₃	54	6	He3:5S3:4C3	486,172

Non-split extensions G=N.Q with N=He₃⋊₅S₃ and Q=C₃

extension	φ:Q→Out N	d	ρ	Label	ID
He₃⋊₅S₃.₁C₃ = C₃²⋊C₉⋊S₃	φ: C₃/C₁ → C₃ ⊆ Out He₃⋊₅S₃	18	6	He3:5S3.1C3	486,7
He₃⋊₅S₃.₂C₃ = (C₃×He₃).C₆	φ: C₃/C₁ → C₃ ⊆ Out He₃⋊₅S₃	54	6	He3:5S3.2C3	486,9
He₃⋊₅S₃.₃C₃ = (C₃²×C₉)⋊₈S₃	φ: C₃/C₁ → C₃ ⊆ Out He₃⋊₅S₃	54	6	He3:5S3.3C3	486,150
He₃⋊₅S₃.₄C₃ = He₃.C₃⋊S₃	φ: C₃/C₁ → C₃ ⊆ Out He₃⋊₅S₃	54	6	He3:5S3.4C3	486,169
He₃⋊₅S₃.₅C₃ = C₉○He₃⋊₄S₃	φ: trivial image	54	6	He3:5S3.5C3	486,246

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