Extensions 1→N→G→Q→1 with N=He₃ and Q=C₁₂

Direct product G=N×Q with N=He₃ and Q=C₁₂

		d	ρ	Label	ID
C₁₂×He₃		108		C12xHe3	324,106

Semidirect products G=N:Q with N=He₃ and Q=C₁₂

extension	φ:Q→Out N	d	ρ	Label	ID
He₃⋊C₁₂ = He₃⋊C₁₂	φ: C₁₂/C₂ → C₆ ⊆ Out He₃	36	3	He3:C12	324,13
He₃⋊₂C₁₂ = C₃×He₃⋊C₄	φ: C₁₂/C₃ → C₄ ⊆ Out He₃	54		He3:2C12	324,110
He₃⋊₃C₁₂ = C₄×C₃≀C₃	φ: C₁₂/C₄ → C₃ ⊆ Out He₃	36	3	He3:3C12	324,31
He₃⋊₄C₁₂ = C₄×He₃⋊C₃	φ: C₁₂/C₄ → C₃ ⊆ Out He₃	108	3	He3:4C12	324,33
He₃⋊₅C₁₂ = C₃×C₃²⋊C₁₂	φ: C₁₂/C₆ → C₂ ⊆ Out He₃	36	6	He3:5C12	324,92
He₃⋊₆C₁₂ = C₃×He₃⋊₃C₄	φ: C₁₂/C₆ → C₂ ⊆ Out He₃	108		He3:6C12	324,99

Non-split extensions G=N.Q with N=He₃ and Q=C₁₂

extension	φ:Q→Out N	d	ρ	Label	ID
He₃.₁C₁₂ = He₃.C₁₂	φ: C₁₂/C₂ → C₆ ⊆ Out He₃	108	3	He3.1C12	324,15
He₃.₂C₁₂ = He₃.₂C₁₂	φ: C₁₂/C₂ → C₆ ⊆ Out He₃	108	3	He3.2C12	324,17
He₃.₃C₁₂ = He₃.₃C₁₂	φ: C₁₂/C₃ → C₄ ⊆ Out He₃	54	3	He3.3C12	324,111
He₃.₄C₁₂ = C₄×He₃.C₃	φ: C₁₂/C₄ → C₃ ⊆ Out He₃	108	3	He3.4C12	324,32
He₃.₅C₁₂ = He₃.₅C₁₂	φ: C₁₂/C₆ → C₂ ⊆ Out He₃	108	3	He3.5C12	324,102
He₃.₆C₁₂ = C₄×C₉○He₃	φ: trivial image	108	3	He3.6C12	324,108

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