Extensions 1→N→G→Q→1 with N=C₃ and Q=S₃xHe₃

Direct product G=NxQ with N=C₃ and Q=S₃xHe₃

		d	ρ	Label	ID
C₃xS₃xHe₃		54		C3xS3xHe3	486,223

Semidirect products G=N:Q with N=C₃ and Q=S₃xHe₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃:(S₃xHe₃) = C₃:S₃xHe₃	φ: S₃xHe₃/C₃xHe₃ → C₂ ⊆ Aut C₃	54		C3:(S3xHe3)	486,231

Non-split extensions G=N.Q with N=C₃ and Q=S₃xHe₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(S₃xHe₃) = D₉xHe₃	φ: S₃xHe₃/C₃xHe₃ → C₂ ⊆ Aut C₃	54	6	C3.1(S3xHe3)	486,99
C₃.₂(S₃xHe₃) = C₃⁴:C₆	φ: S₃xHe₃/C₃xHe₃ → C₂ ⊆ Aut C₃	18	6	C3.2(S3xHe3)	486,102
C₃.₃(S₃xHe₃) = D₉:He₃	φ: S₃xHe₃/C₃xHe₃ → C₂ ⊆ Aut C₃	54	6	C3.3(S3xHe3)	486,106
C₃.₄(S₃xHe₃) = S₃xC₃²:C₉	central extension (φ=1)	54		C3.4(S3xHe3)	486,95
C₃.₅(S₃xHe₃) = S₃xC₃wrC₃	central stem extension (φ=1)	18	6	C3.5(S3xHe3)	486,117
C₃.₆(S₃xHe₃) = S₃xHe₃.C₃	central stem extension (φ=1)	54	6	C3.6(S3xHe3)	486,120
C₃.₇(S₃xHe₃) = S₃xHe₃:C₃	central stem extension (φ=1)	54	6	C3.7(S3xHe3)	486,123
C₃.₈(S₃xHe₃) = S₃xC₃.He₃	central stem extension (φ=1)	54	6	C3.8(S3xHe3)	486,124

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