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

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

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

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

extension	φ:Q→Out N	d	ρ	Label	ID
(C₃×C₃⋊D₄)⋊₁S₃ = C₆².₉₀D₆	φ: S₃/C₃ → C₂ ⊆ Out C₃×C₃⋊D₄	72		(C3xC3:D4):1S3	432,675
(C₃×C₃⋊D₄)⋊₂S₃ = C₆².₉₁D₆	φ: S₃/C₃ → C₂ ⊆ Out C₃×C₃⋊D₄	72		(C3xC3:D4):2S3	432,676
(C₃×C₃⋊D₄)⋊₃S₃ = C₃⋊S₃×C₃⋊D₄	φ: S₃/C₃ → C₂ ⊆ Out C₃×C₃⋊D₄	72		(C3xC3:D4):3S3	432,685
(C₃×C₃⋊D₄)⋊₄S₃ = C₆²⋊₂₃D₆	φ: S₃/C₃ → C₂ ⊆ Out C₃×C₃⋊D₄	36		(C3xC3:D4):4S3	432,686
(C₃×C₃⋊D₄)⋊₅S₃ = C₃×D₆.₄D₆	φ: S₃/C₃ → C₂ ⊆ Out C₃×C₃⋊D₄	24	4	(C3xC3:D4):5S3	432,653
(C₃×C₃⋊D₄)⋊₆S₃ = C₃×Dic₃⋊D₆	φ: S₃/C₃ → C₂ ⊆ Out C₃×C₃⋊D₄	24	4	(C3xC3:D4):6S3	432,659
(C₃×C₃⋊D₄)⋊₇S₃ = C₃×D₆.₃D₆	φ: trivial image	24	4	(C3xC3:D4):7S3	432,652

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

extension	φ:Q→Out N	d	ρ	Label	ID
(C₃×C₃⋊D₄).₁S₃ = Dic₃.D₁₈	φ: S₃/C₃ → C₂ ⊆ Out C₃×C₃⋊D₄	72	4	(C3xC3:D4).1S3	432,309
(C₃×C₃⋊D₄).₂S₃ = D₁₈.₄D₆	φ: S₃/C₃ → C₂ ⊆ Out C₃×C₃⋊D₄	72	4-	(C3xC3:D4).2S3	432,310
(C₃×C₃⋊D₄).₃S₃ = D₉×C₃⋊D₄	φ: S₃/C₃ → C₂ ⊆ Out C₃×C₃⋊D₄	72	4	(C3xC3:D4).3S3	432,314
(C₃×C₃⋊D₄).₄S₃ = D₁₈⋊D₆	φ: S₃/C₃ → C₂ ⊆ Out C₃×C₃⋊D₄	36	4+	(C3xC3:D4).4S3	432,315

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