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

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

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

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(He₃⋊₅S₃) = C₃⁴⋊₁₃S₃	φ: He₃⋊₅S₃/C₃×He₃ → C₂ ⊆ Aut C₃	54		C3:(He3:5S3)	486,248

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(He₃⋊₅S₃) = C₃³⋊₆D₉	φ: He₃⋊₅S₃/C₃×He₃ → C₂ ⊆ Aut C₃	54		C3.1(He3:5S3)	486,181
C₃.₂(He₃⋊₅S₃) = He₃⋊₄D₉	φ: He₃⋊₅S₃/C₃×He₃ → C₂ ⊆ Aut C₃	54	6	C3.2(He3:5S3)	486,182
C₃.₃(He₃⋊₅S₃) = C₃⁴⋊₇S₃	φ: He₃⋊₅S₃/C₃×He₃ → C₂ ⊆ Aut C₃	27		C3.3(He3:5S3)	486,185
C₃.₄(He₃⋊₅S₃) = He₃.(C₃⋊S₃)	φ: He₃⋊₅S₃/C₃×He₃ → C₂ ⊆ Aut C₃	81		C3.4(He3:5S3)	486,186
C₃.₅(He₃⋊₅S₃) = C₃⋊(He₃⋊S₃)	φ: He₃⋊₅S₃/C₃×He₃ → C₂ ⊆ Aut C₃	81		C3.5(He3:5S3)	486,187
C₃.₆(He₃⋊₅S₃) = (C₃²×C₉).S₃	φ: He₃⋊₅S₃/C₃×He₃ → C₂ ⊆ Aut C₃	81		C3.6(He3:5S3)	486,188
C₃.₇(He₃⋊₅S₃) = C₃≀C₃⋊S₃	φ: He₃⋊₅S₃/C₃×He₃ → C₂ ⊆ Aut C₃	27	6+	C3.7(He3:5S3)	486,189
C₃.₈(He₃⋊₅S₃) = C₃⁴⋊₆S₃	central stem extension (φ=1)	27		C3.8(He3:5S3)	486,183

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