Extensions 1→N→G→Q→1 with N=C₃×S₃ and Q=C₃⋊D₄

Direct product G=N×Q with N=C₃×S₃ and Q=C₃⋊D₄

		d	ρ	Label	ID
C₃×S₃×C₃⋊D₄		24	4	C3xS3xC3:D4	432,658

Semidirect products G=N:Q with N=C₃×S₃ and Q=C₃⋊D₄

extension	φ:Q→Out N	d	ρ	Label	ID
(C₃×S₃)⋊₁(C₃⋊D₄) = S₃×C₃⋊D₁₂	φ: C₃⋊D₄/Dic₃ → C₂ ⊆ Out C₃×S₃	24	8+	(C3xS3):1(C3:D4)	432,598
(C₃×S₃)⋊₂(C₃⋊D₄) = S₃×D₆⋊S₃	φ: C₃⋊D₄/D₆ → C₂ ⊆ Out C₃×S₃	48	8-	(C3xS3):2(C3:D4)	432,597
(C₃×S₃)⋊₃(C₃⋊D₄) = S₃×C₃²⋊₇D₄	φ: C₃⋊D₄/C₂×C₆ → C₂ ⊆ Out C₃×S₃	72		(C3xS3):3(C3:D4)	432,684

Non-split extensions G=N.Q with N=C₃×S₃ and Q=C₃⋊D₄

extension	φ:Q→Out N	d	ρ	Label	ID
(C₃×S₃).(C₃⋊D₄) = S₃×C₉⋊D₄	φ: C₃⋊D₄/C₂×C₆ → C₂ ⊆ Out C₃×S₃	72	4	(C3xS3).(C3:D4)	432,313

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C3×S3 and Q=C3⋊D4