Extensions 1→N→G→Q→1 with N=He₃ and Q=D₆

Direct product G=N×Q with N=He₃ and Q=D₆

		d	ρ	Label	ID
C₂×S₃×He₃		36	6	C2xS3xHe3	324,139

Semidirect products G=N:Q with N=He₃ and Q=D₆

extension	φ:Q→Out N	d	ρ	Label	ID
He₃⋊D₆ = He₃⋊D₆	φ: D₆/C₁ → D₆ ⊆ Out He₃	9	6+	He3:D6	324,39
He₃⋊₂D₆ = C₂×C₃³⋊C₆	φ: D₆/C₂ → S₃ ⊆ Out He₃	18	6+	He3:2D6	324,69
He₃⋊₃D₆ = C₂×C₃³⋊S₃	φ: D₆/C₂ → S₃ ⊆ Out He₃	18	6+	He3:3D6	324,77
He₃⋊₄D₆ = C₂×He₃⋊S₃	φ: D₆/C₂ → S₃ ⊆ Out He₃	54	6+	He3:4D6	324,79
He₃⋊₅D₆ = He₃⋊₅D₆	φ: D₆/C₃ → C₂² ⊆ Out He₃	18	12+	He3:5D6	324,121
He₃⋊₆D₆ = He₃⋊₆D₆	φ: D₆/C₃ → C₂² ⊆ Out He₃	27		He3:6D6	324,124
He₃⋊₇D₆ = S₃×C₃²⋊C₆	φ: D₆/S₃ → C₂ ⊆ Out He₃	18	12+	He3:7D6	324,116
He₃⋊₈D₆ = S₃×He₃⋊C₂	φ: D₆/S₃ → C₂ ⊆ Out He₃	18	6	He3:8D6	324,122
He₃⋊₉D₆ = C₂×He₃⋊₄S₃	φ: D₆/C₆ → C₂ ⊆ Out He₃	54		He3:9D6	324,144
He₃⋊₁₀D₆ = C₂×He₃⋊₅S₃	φ: D₆/C₆ → C₂ ⊆ Out He₃	36	6	He3:10D6	324,150

Non-split extensions G=N.Q with N=He₃ and Q=D₆

extension	φ:Q→Out N	d	ρ	Label	ID
He₃.₁D₆ = He₃.D₆	φ: D₆/C₁ → D₆ ⊆ Out He₃	27	6+	He3.1D6	324,40
He₃.₂D₆ = He₃.₂D₆	φ: D₆/C₁ → D₆ ⊆ Out He₃	27	6+	He3.2D6	324,41
He₃.₃D₆ = C₂×He₃.S₃	φ: D₆/C₂ → S₃ ⊆ Out He₃	54	6+	He3.3D6	324,71
He₃.₄D₆ = C₂×He₃.₂S₃	φ: D₆/C₂ → S₃ ⊆ Out He₃	54	6+	He3.4D6	324,73
He₃.₅D₆ = C₂×He₃.₃S₃	φ: D₆/C₂ → S₃ ⊆ Out He₃	54	6+	He3.5D6	324,78
He₃.₆D₆ = He₃.₆D₆	φ: D₆/C₃ → C₂² ⊆ Out He₃	27	6+	He3.6D6	324,125
He₃.₇D₆ = C₂×He₃.₄S₃	φ: D₆/C₆ → C₂ ⊆ Out He₃	54	6+	He3.7D6	324,147

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁