Extensions 1→N→G→Q→1 with N=C₃.He₃ and Q=C₆

Direct product G=NxQ with N=C₃.He₃ and Q=C₆

		d	ρ	Label	ID
C₆xC₃.He₃		162		C6xC3.He3	486,213

Semidirect products G=N:Q with N=C₃.He₃ and Q=C₆

extension	φ:Q→Out N	d	ρ	Label	ID
C₃.He₃:C₆ = C₃.He₃:C₆	φ: C₆/C₁ → C₆ ⊆ Out C₃.He₃	27	18+	C3.He3:C6	486,179
C₃.He₃:₂C₆ = C₂xC₉²:C₃	φ: C₆/C₂ → C₃ ⊆ Out C₃.He₃	54	3	C3.He3:2C6	486,85
C₃.He₃:₃C₆ = C₂xC₃².He₃	φ: C₆/C₂ → C₃ ⊆ Out C₃.He₃	54	9	C3.He3:3C6	486,88
C₃.He₃:₄C₆ = C₂xC₃².₆He₃	φ: C₆/C₂ → C₃ ⊆ Out C₃.He₃	54	9	C3.He3:4C6	486,90
C₃.He₃:₅C₆ = C₂xC₃².C₃³	φ: C₆/C₂ → C₃ ⊆ Out C₃.He₃	54	9	C3.He3:5C6	486,218
C₃.He₃:₆C₆ = C₂xC₉.₂He₃	φ: C₆/C₂ → C₃ ⊆ Out C₃.He₃	54	9	C3.He3:6C6	486,219
C₃.He₃:₇C₆ = C₃x3_-¹⁺².S₃	φ: C₆/C₃ → C₂ ⊆ Out C₃.He₃	54	6	C3.He3:7C6	486,174
C₃.He₃:₈C₆ = C₂xC₉.He₃	φ: trivial image	54	3	C3.He3:8C6	486,214

Non-split extensions G=N.Q with N=C₃.He₃ and Q=C₆

extension	φ:Q→Out N	d	ρ	Label	ID
C₃.He₃.₁C₆ = C₉².S₃	φ: C₆/C₁ → C₆ ⊆ Out C₃.He₃	27	6+	C3.He3.1C6	486,38
C₃.He₃.₂C₆ = C₉:C₉.S₃	φ: C₆/C₁ → C₆ ⊆ Out C₃.He₃	27	18+	C3.He3.2C6	486,39
C₃.He₃.₃C₆ = C₉:C₉.₃S₃	φ: C₆/C₁ → C₆ ⊆ Out C₃.He₃	27	18+	C3.He3.3C6	486,40
C₃.He₃.₄C₆ = C₂xC₉².C₃	φ: C₆/C₂ → C₃ ⊆ Out C₃.He₃	54	3	C3.He3.4C6	486,87
C₃.He₃.₅C₆ = C₂xC₃².₅He₃	φ: C₆/C₂ → C₃ ⊆ Out C₃.He₃	54	9	C3.He3.5C6	486,89

׿

x

:

Z

F

o

wr

Q

<