Extensions 1→N→G→Q→1 with N=C₃ and Q=C₃×Q₈⋊₃S₃

Direct product G=N×Q with N=C₃ and Q=C₃×Q₈⋊₃S₃

		d	ρ	Label	ID
C₃²×Q₈⋊₃S₃		144		C3^2xQ8:3S3	432,707

Semidirect products G=N:Q with N=C₃ and Q=C₃×Q₈⋊₃S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₃×Q₈⋊₃S₃) = C₃×D₆.₆D₆	φ: C₃×Q₈⋊₃S₃/S₃×C₁₂ → C₂ ⊆ Aut C₃	48	4	C3:1(C3xQ8:3S3)	432,647
C₃⋊₂(C₃×Q₈⋊₃S₃) = C₃×D₁₂⋊S₃	φ: C₃×Q₈⋊₃S₃/C₃×D₁₂ → C₂ ⊆ Aut C₃	48	4	C3:2(C3xQ8:3S3)	432,644
C₃⋊₃(C₃×Q₈⋊₃S₃) = C₃×C₁₂.₂₆D₆	φ: C₃×Q₈⋊₃S₃/Q₈×C₃² → C₂ ⊆ Aut C₃	144		C3:3(C3xQ8:3S3)	432,717

Non-split extensions G=N.Q with N=C₃ and Q=C₃×Q₈⋊₃S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₃×Q₈⋊₃S₃) = C₃×Q₈⋊₃D₉	φ: C₃×Q₈⋊₃S₃/Q₈×C₃² → C₂ ⊆ Aut C₃	144	4	C3.1(C3xQ8:3S3)	432,365
C₃.₂(C₃×Q₈⋊₃S₃) = (Q₈×He₃)⋊C₂	φ: C₃×Q₈⋊₃S₃/Q₈×C₃² → C₂ ⊆ Aut C₃	72	12+	C3.2(C3xQ8:3S3)	432,369
C₃.₃(C₃×Q₈⋊₃S₃) = D₃₆⋊₃C₆	φ: C₃×Q₈⋊₃S₃/Q₈×C₃² → C₂ ⊆ Aut C₃	72	12+	C3.3(C3xQ8:3S3)	432,371
C₃.₄(C₃×Q₈⋊₃S₃) = C₉×Q₈⋊₃S₃	central extension (φ=1)	144	4	C3.4(C3xQ8:3S3)	432,367

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