Extensions 1→N→G→Q→1 with N=C₃ and Q=C₃×Q₈⋊₂S₃

Direct product G=N×Q with N=C₃ and Q=C₃×Q₈⋊₂S₃

		d	ρ	Label	ID
C₃²×Q₈⋊₂S₃		144		C3^2xQ8:2S3	432,477

Semidirect products G=N:Q with N=C₃ and Q=C₃×Q₈⋊₂S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₃×Q₈⋊₂S₃) = C₃×C₃²⋊₅SD₁₆	φ: C₃×Q₈⋊₂S₃/C₃×C₃⋊C₈ → C₂ ⊆ Aut C₃	48	4	C3:1(C3xQ8:2S3)	432,422
C₃⋊₂(C₃×Q₈⋊₂S₃) = C₃×Dic₆⋊S₃	φ: C₃×Q₈⋊₂S₃/C₃×D₁₂ → C₂ ⊆ Aut C₃	48	4	C3:2(C3xQ8:2S3)	432,420
C₃⋊₃(C₃×Q₈⋊₂S₃) = C₃×C₃²⋊₁₁SD₁₆	φ: C₃×Q₈⋊₂S₃/Q₈×C₃² → C₂ ⊆ Aut C₃	144		C3:3(C3xQ8:2S3)	432,493

Non-split extensions G=N.Q with N=C₃ and Q=C₃×Q₈⋊₂S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₃×Q₈⋊₂S₃) = C₃×Q₈⋊₂D₉	φ: C₃×Q₈⋊₂S₃/Q₈×C₃² → C₂ ⊆ Aut C₃	144	4	C3.1(C3xQ8:2S3)	432,157
C₃.₂(C₃×Q₈⋊₂S₃) = He₃⋊₁₀SD₁₆	φ: C₃×Q₈⋊₂S₃/Q₈×C₃² → C₂ ⊆ Aut C₃	72	12+	C3.2(C3xQ8:2S3)	432,161
C₃.₃(C₃×Q₈⋊₂S₃) = D₃₆.C₆	φ: C₃×Q₈⋊₂S₃/Q₈×C₃² → C₂ ⊆ Aut C₃	72	12+	C3.3(C3xQ8:2S3)	432,163
C₃.₄(C₃×Q₈⋊₂S₃) = C₉×Q₈⋊₂S₃	central extension (φ=1)	144	4	C3.4(C3xQ8:2S3)	432,158

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