Extensions 1→N→G→Q→1 with N=He₃ and Q=C₃xC₆

Direct product G=NxQ with N=He₃ and Q=C₃xC₆

		d	ρ	Label	ID
C₃xC₆xHe₃		162		C3xC6xHe3	486,251

Semidirect products G=N:Q with N=He₃ and Q=C₃xC₆

extension	φ:Q→Out N	d	ρ	Label	ID
He₃:(C₃xC₆) = C₃xC₃wrS₃	φ: C₃xC₆/C₃ → C₆ ⊆ Out He₃	27		He3:(C3xC6)	486,115
He₃:₂(C₃xC₆) = C₆xC₃wrC₃	φ: C₃xC₆/C₆ → C₃ ⊆ Out He₃	54		He3:2(C3xC6)	486,210
He₃:₃(C₃xC₆) = C₆xHe₃:C₃	φ: C₃xC₆/C₆ → C₃ ⊆ Out He₃	162		He3:3(C3xC6)	486,212
He₃:₄(C₃xC₆) = C₂xHe₃:C₃²	φ: C₃xC₆/C₆ → C₃ ⊆ Out He₃	54	9	He3:4(C3xC6)	486,217
He₃:₅(C₃xC₆) = C₃²xC₃²:C₆	φ: C₃xC₆/C₃² → C₂ ⊆ Out He₃	54		He3:5(C3xC6)	486,222
He₃:₆(C₃xC₆) = C₃²xHe₃:C₂	φ: C₃xC₆/C₃² → C₂ ⊆ Out He₃	81		He3:6(C3xC6)	486,230
He₃:₇(C₃xC₆) = C₂x3₊¹⁺⁴	φ: trivial image	54	9	He3:7(C3xC6)	486,254

Non-split extensions G=N.Q with N=He₃ and Q=C₃xC₆

extension	φ:Q→Out N	d	ρ	Label	ID
He₃.₁(C₃xC₆) = C₃xHe₃.C₆	φ: C₃xC₆/C₃ → C₆ ⊆ Out He₃	81		He3.1(C3xC6)	486,118
He₃.₂(C₃xC₆) = C₃xHe₃.₂C₆	φ: C₃xC₆/C₃ → C₆ ⊆ Out He₃	81		He3.2(C3xC6)	486,121
He₃.₃(C₃xC₆) = C₃wrS₃:₃C₃	φ: C₃xC₆/C₃ → C₆ ⊆ Out He₃	27	3	He3.3(C3xC6)	486,125
He₃.₄(C₃xC₆) = C₃wrC₃:C₆	φ: C₃xC₆/C₃ → C₆ ⊆ Out He₃	27	9	He3.4(C3xC6)	486,126
He₃.₅(C₃xC₆) = He₃.C₃:C₆	φ: C₃xC₆/C₃ → C₆ ⊆ Out He₃	27	9	He3.5(C3xC6)	486,128
He₃.₆(C₃xC₆) = He₃.(C₃xC₆)	φ: C₃xC₆/C₃ → C₆ ⊆ Out He₃	27	9	He3.6(C3xC6)	486,130
He₃.₇(C₃xC₆) = C₃wrC₃.C₆	φ: C₃xC₆/C₃ → C₆ ⊆ Out He₃	27	9	He3.7(C3xC6)	486,132
He₃.₈(C₃xC₆) = C₆xHe₃.C₃	φ: C₃xC₆/C₆ → C₃ ⊆ Out He₃	162		He3.8(C3xC6)	486,211
He₃.₉(C₃xC₆) = C₂xC₉.He₃	φ: C₃xC₆/C₆ → C₃ ⊆ Out He₃	54	3	He3.9(C3xC6)	486,214
He₃.₁₀(C₃xC₆) = C₂xC₃³:C₃²	φ: C₃xC₆/C₆ → C₃ ⊆ Out He₃	54	9	He3.10(C3xC6)	486,215
He₃.₁₁(C₃xC₆) = C₂xHe₃.C₃²	φ: C₃xC₆/C₆ → C₃ ⊆ Out He₃	54	9	He3.11(C3xC6)	486,216
He₃.₁₂(C₃xC₆) = C₂xC₉.₂He₃	φ: C₃xC₆/C₆ → C₃ ⊆ Out He₃	54	9	He3.12(C3xC6)	486,219
He₃.₁₃(C₃xC₆) = C₃xHe₃.₄C₆	φ: C₃xC₆/C₃² → C₂ ⊆ Out He₃	81		He3.13(C3xC6)	486,235
He₃.₁₄(C₃xC₆) = 3₊¹⁺⁴:₂C₂	φ: C₃xC₆/C₃² → C₂ ⊆ Out He₃	27	9	He3.14(C3xC6)	486,237
He₃.₁₅(C₃xC₆) = 3_-¹⁺⁴:₂C₂	φ: C₃xC₆/C₃² → C₂ ⊆ Out He₃	27	9	He3.15(C3xC6)	486,239
He₃.₁₆(C₃xC₆) = C₆xC₉oHe₃	φ: trivial image	162		He3.16(C3xC6)	486,253
He₃.₁₇(C₃xC₆) = C₂x3_-¹⁺⁴	φ: trivial image	54	9	He3.17(C3xC6)	486,255

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