Extensions 1→N→G→Q→1 with N=C₃ and Q=He₃.₂C₆

Direct product G=N×Q with N=C₃ and Q=He₃.₂C₆

		d	ρ	Label	ID
C₃×He₃.₂C₆		81		C3xHe3.2C6	486,121

Semidirect products G=N:Q with N=C₃ and Q=He₃.₂C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(He₃.₂C₆) = He₃⋊C₃⋊₂S₃	φ: He₃.₂C₆/He₃⋊C₃ → C₂ ⊆ Aut C₃	54	6	C3:(He3.2C6)	486,172

Non-split extensions G=N.Q with N=C₃ and Q=He₃.₂C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(He₃.₂C₆) = C₃²⋊C₉.S₃	φ: He₃.₂C₆/He₃⋊C₃ → C₂ ⊆ Aut C₃	18	6	C3.1(He3.2C6)	486,5
C₃.₂(He₃.₂C₆) = (C₃×He₃).C₆	φ: He₃.₂C₆/He₃⋊C₃ → C₂ ⊆ Aut C₃	54	6	C3.2(He3.2C6)	486,9
C₃.₃(He₃.₂C₆) = C₃²⋊C₉.C₆	φ: He₃.₂C₆/He₃⋊C₃ → C₂ ⊆ Aut C₃	54	6	C3.3(He3.2C6)	486,10
C₃.₄(He₃.₂C₆) = (C₃×C₉)⋊₃D₉	φ: He₃.₂C₆/He₃⋊C₃ → C₂ ⊆ Aut C₃	54	6	C3.4(He3.2C6)	486,23
C₃.₅(He₃.₂C₆) = C₉²⋊S₃	φ: He₃.₂C₆/He₃⋊C₃ → C₂ ⊆ Aut C₃	27	6+	C3.5(He3.2C6)	486,36
C₃.₆(He₃.₂C₆) = C₉².S₃	φ: He₃.₂C₆/He₃⋊C₃ → C₂ ⊆ Aut C₃	27	6+	C3.6(He3.2C6)	486,38
C₃.₇(He₃.₂C₆) = C₉⋊C₉.S₃	φ: He₃.₂C₆/He₃⋊C₃ → C₂ ⊆ Aut C₃	27	18+	C3.7(He3.2C6)	486,39
C₃.₈(He₃.₂C₆) = C₉⋊C₉.₃S₃	φ: He₃.₂C₆/He₃⋊C₃ → C₂ ⊆ Aut C₃	27	18+	C3.8(He3.2C6)	486,40
C₃.₉(He₃.₂C₆) = C₉⋊C₉⋊S₃	φ: He₃.₂C₆/He₃⋊C₃ → C₂ ⊆ Aut C₃	27	18+	C3.9(He3.2C6)	486,41
C₃.₁₀(He₃.₂C₆) = He₃⋊C₁₈	central extension (φ=1)	81		C3.10(He3.2C6)	486,24

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