Extensions 1→N→G→Q→1 with N=C₃ and Q=S₃×He₃

Direct product G=N×Q with N=C₃ and Q=S₃×He₃

		d	ρ	Label	ID
C₃×S₃×He₃		54		C3xS3xHe3	486,223

Semidirect products G=N:Q with N=C₃ and Q=S₃×He₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(S₃×He₃) = C₃⋊S₃×He₃	φ: S₃×He₃/C₃×He₃ → C₂ ⊆ Aut C₃	54		C3:(S3xHe3)	486,231

Non-split extensions G=N.Q with N=C₃ and Q=S₃×He₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(S₃×He₃) = D₉×He₃	φ: S₃×He₃/C₃×He₃ → C₂ ⊆ Aut C₃	54	6	C3.1(S3xHe3)	486,99
C₃.₂(S₃×He₃) = C₃⁴⋊C₆	φ: S₃×He₃/C₃×He₃ → C₂ ⊆ Aut C₃	18	6	C3.2(S3xHe3)	486,102
C₃.₃(S₃×He₃) = D₉⋊He₃	φ: S₃×He₃/C₃×He₃ → C₂ ⊆ Aut C₃	54	6	C3.3(S3xHe3)	486,106
C₃.₄(S₃×He₃) = S₃×C₃²⋊C₉	central extension (φ=1)	54		C3.4(S3xHe3)	486,95
C₃.₅(S₃×He₃) = S₃×C₃≀C₃	central stem extension (φ=1)	18	6	C3.5(S3xHe3)	486,117
C₃.₆(S₃×He₃) = S₃×He₃.C₃	central stem extension (φ=1)	54	6	C3.6(S3xHe3)	486,120
C₃.₇(S₃×He₃) = S₃×He₃⋊C₃	central stem extension (φ=1)	54	6	C3.7(S3xHe3)	486,123
C₃.₈(S₃×He₃) = S₃×C₃.He₃	central stem extension (φ=1)	54	6	C3.8(S3xHe3)	486,124

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