Extensions 1→N→G→Q→1 with N=C₃⋊S₃ and Q=D₆

Direct product G=N×Q with N=C₃⋊S₃ and Q=D₆

		d	ρ	Label	ID
C₂×S₃×C₃⋊S₃		36		C2xS3xC3:S3	216,171

Semidirect products G=N:Q with N=C₃⋊S₃ and Q=D₆

extension	φ:Q→Out N	d	ρ	Label	ID
C₃⋊S₃⋊D₆ = C₂×C₃²⋊D₆	φ: D₆/C₂ → S₃ ⊆ Out C₃⋊S₃	18	6+	C3:S3:D6	216,102
C₃⋊S₃⋊₂D₆ = S₃³	φ: D₆/S₃ → C₂ ⊆ Out C₃⋊S₃	12	8+	C3:S3:2D6	216,162
C₃⋊S₃⋊₃D₆ = C₂×C₃²⋊₄D₆	φ: D₆/C₆ → C₂ ⊆ Out C₃⋊S₃	24	4	C3:S3:3D6	216,172

Non-split extensions G=N.Q with N=C₃⋊S₃ and Q=D₆

extension	φ:Q→Out N	d	ρ	Label	ID
C₃⋊S₃.₁D₆ = C₃³⋊D₄	φ: D₆/C₃ → C₂² ⊆ Out C₃⋊S₃	12	4	C3:S3.1D6	216,158
C₃⋊S₃.₂D₆ = C₃²⋊₂D₁₂	φ: D₆/C₃ → C₂² ⊆ Out C₃⋊S₃	12	8+	C3:S3.2D6	216,159
C₃⋊S₃.₃D₆ = C₃³⋊Q₈	φ: D₆/C₃ → C₂² ⊆ Out C₃⋊S₃	24	8	C3:S3.3D6	216,161
C₃⋊S₃.₄D₆ = S₃×C₃²⋊C₄	φ: D₆/S₃ → C₂ ⊆ Out C₃⋊S₃	12	8+	C3:S3.4D6	216,156
C₃⋊S₃.₅D₆ = C₂×C₃³⋊C₄	φ: D₆/C₆ → C₂ ⊆ Out C₃⋊S₃	24	4	C3:S3.5D6	216,169

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁