Extensions 1→N→G→Q→1 with N=He₃ and Q=C₃²

Direct product G=N×Q with N=He₃ and Q=C₃²

		d	ρ	Label	ID
C₃²×He₃		81		C3^2xHe3	243,62

Semidirect products G=N:Q with N=He₃ and Q=C₃²

extension	φ:Q→Out N	d	ρ	Label	ID
He₃⋊₁C₃² = C₃×C₃≀C₃	φ: C₃²/C₃ → C₃ ⊆ Out He₃	27		He3:1C3^2	243,51
He₃⋊₂C₃² = C₃×He₃⋊C₃	φ: C₃²/C₃ → C₃ ⊆ Out He₃	81		He3:2C3^2	243,53
He₃⋊₃C₃² = He₃⋊C₃²	φ: C₃²/C₃ → C₃ ⊆ Out He₃	27	9	He3:3C3^2	243,58
He₃⋊₄C₃² = 3₊¹⁺⁴	φ: trivial image	27	9	He3:4C3^2	243,65

Non-split extensions G=N.Q with N=He₃ and Q=C₃²

extension	φ:Q→Out N	d	ρ	Label	ID
He₃.₁C₃² = C₃×He₃.C₃	φ: C₃²/C₃ → C₃ ⊆ Out He₃	81		He3.1C3^2	243,52
He₃.₂C₃² = C₉.He₃	φ: C₃²/C₃ → C₃ ⊆ Out He₃	27	3	He3.2C3^2	243,55
He₃.₃C₃² = C₃³⋊C₃²	φ: C₃²/C₃ → C₃ ⊆ Out He₃	27	9	He3.3C3^2	243,56
He₃.₄C₃² = He₃.C₃²	φ: C₃²/C₃ → C₃ ⊆ Out He₃	27	9	He3.4C3^2	243,57
He₃.₅C₃² = C₉.₂He₃	φ: C₃²/C₃ → C₃ ⊆ Out He₃	27	9	He3.5C3^2	243,60
He₃.₆C₃² = C₃×C₉○He₃	φ: trivial image	81		He3.6C3^2	243,64
He₃.₇C₃² = 3_-¹⁺⁴	φ: trivial image	27	9	He3.7C3^2	243,66

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