Extensions 1→N→G→Q→1 with N=He₃⋊C₂ and Q=C₃²

Direct product G=N×Q with N=He₃⋊C₂ and Q=C₃²

		d	ρ	Label	ID
C₃²×He₃⋊C₂		81		C3^2xHe3:C2	486,230

Semidirect products G=N:Q with N=He₃⋊C₂ and Q=C₃²

extension	φ:Q→Out N	d	ρ	Label	ID
He₃⋊C₂⋊₁C₃² = C₃×C₃≀S₃	φ: C₃²/C₃ → C₃ ⊆ Out He₃⋊C₂	27		He3:C2:1C3^2	486,115
He₃⋊C₂⋊₂C₃² = C₃×He₃.₂C₆	φ: C₃²/C₃ → C₃ ⊆ Out He₃⋊C₂	81		He3:C2:2C3^2	486,121
He₃⋊C₂⋊₃C₃² = He₃.(C₃×C₆)	φ: C₃²/C₃ → C₃ ⊆ Out He₃⋊C₂	27	9	He3:C2:3C3^2	486,130
He₃⋊C₂⋊₄C₃² = 3₊¹⁺⁴⋊₂C₂	φ: trivial image	27	9	He3:C2:4C3^2	486,237

Non-split extensions G=N.Q with N=He₃⋊C₂ and Q=C₃²

extension	φ:Q→Out N	d	ρ	Label	ID
He₃⋊C₂.₁C₃² = C₃×He₃.C₆	φ: C₃²/C₃ → C₃ ⊆ Out He₃⋊C₂	81		He3:C2.1C3^2	486,118
He₃⋊C₂.₂C₃² = C₃≀S₃⋊₃C₃	φ: C₃²/C₃ → C₃ ⊆ Out He₃⋊C₂	27	3	He3:C2.2C3^2	486,125
He₃⋊C₂.₃C₃² = C₃≀C₃⋊C₆	φ: C₃²/C₃ → C₃ ⊆ Out He₃⋊C₂	27	9	He3:C2.3C3^2	486,126
He₃⋊C₂.₄C₃² = He₃.C₃⋊C₆	φ: C₃²/C₃ → C₃ ⊆ Out He₃⋊C₂	27	9	He3:C2.4C3^2	486,128
He₃⋊C₂.₅C₃² = C₃≀C₃.C₆	φ: C₃²/C₃ → C₃ ⊆ Out He₃⋊C₂	27	9	He3:C2.5C3^2	486,132
He₃⋊C₂.₆C₃² = C₃×He₃.₄C₆	φ: trivial image	81		He3:C2.6C3^2	486,235
He₃⋊C₂.₇C₃² = 3_-¹⁺⁴⋊₂C₂	φ: trivial image	27	9	He3:C2.7C3^2	486,239

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