Extensions 1→N→G→Q→1 with N=C₃ and Q=C₃×C₉⋊S₃

Direct product G=N×Q with N=C₃ and Q=C₃×C₉⋊S₃

		d	ρ	Label	ID
C₃²×C₉⋊S₃		54		C3^2xC9:S3	486,227

Semidirect products G=N:Q with N=C₃ and Q=C₃×C₉⋊S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(C₃×C₉⋊S₃) = C₃×C₃²⋊₄D₉	φ: C₃×C₉⋊S₃/C₃²×C₉ → C₂ ⊆ Aut C₃	162		C3:(C3xC9:S3)	486,240

Non-split extensions G=N.Q with N=C₃ and Q=C₃×C₉⋊S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₃×C₉⋊S₃) = C₃×C₉⋊D₉	φ: C₃×C₉⋊S₃/C₃²×C₉ → C₂ ⊆ Aut C₃	162		C3.1(C3xC9:S3)	486,134
C₃.₂(C₃×C₉⋊S₃) = C₃³⋊D₉	φ: C₃×C₉⋊S₃/C₃²×C₉ → C₂ ⊆ Aut C₃	81		C3.2(C3xC9:S3)	486,137
C₃.₃(C₃×C₉⋊S₃) = C₉²⋊₃C₆	φ: C₃×C₉⋊S₃/C₃²×C₉ → C₂ ⊆ Aut C₃	81		C3.3(C3xC9:S3)	486,141
C₃.₄(C₃×C₉⋊S₃) = He₃⋊₃D₉	φ: C₃×C₉⋊S₃/C₃²×C₉ → C₂ ⊆ Aut C₃	81		C3.4(C3xC9:S3)	486,142
C₃.₅(C₃×C₉⋊S₃) = C₉²⋊₉C₆	φ: C₃×C₉⋊S₃/C₃²×C₉ → C₂ ⊆ Aut C₃	81		C3.5(C3xC9:S3)	486,144
C₃.₆(C₃×C₉⋊S₃) = C₃×C₂₇⋊S₃	φ: C₃×C₉⋊S₃/C₃²×C₉ → C₂ ⊆ Aut C₃	162		C3.6(C3xC9:S3)	486,160
C₃.₇(C₃×C₉⋊S₃) = C₃³.₅D₉	φ: C₃×C₉⋊S₃/C₃²×C₉ → C₂ ⊆ Aut C₃	81		C3.7(C3xC9:S3)	486,162
C₃.₈(C₃×C₉⋊S₃) = He₃.₅D₉	φ: C₃×C₉⋊S₃/C₃²×C₉ → C₂ ⊆ Aut C₃	81	6+	C3.8(C3xC9:S3)	486,163
C₃.₉(C₃×C₉⋊S₃) = C₉×C₉⋊S₃	central extension (φ=1)	54		C3.9(C3xC9:S3)	486,133
C₃.₁₀(C₃×C₉⋊S₃) = C₃×C₃²⋊₂D₉	central stem extension (φ=1)	54		C3.10(C3xC9:S3)	486,135
C₃.₁₁(C₃×C₉⋊S₃) = C₉²⋊₄S₃	central stem extension (φ=1)	54	6	C3.11(C3xC9:S3)	486,140

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁