Extensions 1→N→G→Q→1 with N=He₃ and Q=C₁₈

Direct product G=N×Q with N=He₃ and Q=C₁₈

		d	ρ	Label	ID
C₁₈×He₃		162		C18xHe3	486,194

Semidirect products G=N:Q with N=He₃ and Q=C₁₈

extension	φ:Q→Out N	d	ρ	Label	ID
He₃⋊C₁₈ = He₃⋊C₁₈	φ: C₁₈/C₃ → C₆ ⊆ Out He₃	81		He3:C18	486,24
He₃⋊₂C₁₈ = C₂×He₃⋊C₉	φ: C₁₈/C₆ → C₃ ⊆ Out He₃	162		He3:2C18	486,77
He₃⋊₃C₁₈ = C₉×C₃²⋊C₆	φ: C₁₈/C₉ → C₂ ⊆ Out He₃	54	6	He3:3C18	486,98
He₃⋊₄C₁₈ = C₉×He₃⋊C₂	φ: C₁₈/C₉ → C₂ ⊆ Out He₃	81		He3:4C18	486,143

Non-split extensions G=N.Q with N=He₃ and Q=C₁₈

extension	φ:Q→Out N	d	ρ	Label	ID
He₃.₁C₁₈ = He₃.C₁₈	φ: C₁₈/C₃ → C₆ ⊆ Out He₃	81	3	He3.1C18	486,26
He₃.₂C₁₈ = He₃.₂C₁₈	φ: C₁₈/C₃ → C₆ ⊆ Out He₃	81	3	He3.2C18	486,28
He₃.₃C₁₈ = C₂×C₉.₅He₃	φ: C₁₈/C₆ → C₃ ⊆ Out He₃	162	3	He3.3C18	486,79
He₃.₄C₁₈ = C₂×C₉.₆He₃	φ: C₁₈/C₆ → C₃ ⊆ Out He₃	162	3	He3.4C18	486,80
He₃.₅C₁₈ = He₃.₅C₁₈	φ: C₁₈/C₉ → C₂ ⊆ Out He₃	81	3	He3.5C18	486,164
He₃.₆C₁₈ = C₂×C₂₇○He₃	φ: trivial image	162	3	He3.6C18	486,209

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁