Extensions 1→N→G→Q→1 with N=C₃² and Q=C₃×D₇

Direct product G=N×Q with N=C₃² and Q=C₃×D₇

		d	ρ	Label	ID
D₇×C₃³		189		D7xC3^3	378,53

Semidirect products G=N:Q with N=C₃² and Q=C₃×D₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃²⋊(C₃×D₇) = He₃⋊D₇	φ: C₃×D₇/C₇ → C₆ ⊆ Aut C₃²	63	6+	C3^2:(C3xD7)	378,38
C₃²⋊₂(C₃×D₇) = D₇×He₃	φ: C₃×D₇/D₇ → C₃ ⊆ Aut C₃²	63	6	C3^2:2(C3xD7)	378,30
C₃²⋊₃(C₃×D₇) = C₃²×D₂₁	φ: C₃×D₇/C₂₁ → C₂ ⊆ Aut C₃²	126		C3^2:3(C3xD7)	378,55
C₃²⋊₄(C₃×D₇) = C₃×C₃⋊D₂₁	φ: C₃×D₇/C₂₁ → C₂ ⊆ Aut C₃²	126		C3^2:4(C3xD7)	378,57

Non-split extensions G=N.Q with N=C₃² and Q=C₃×D₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃².(C₃×D₇) = D₇×3_-¹⁺²	φ: C₃×D₇/D₇ → C₃ ⊆ Aut C₃²	63	6	C3^2.(C3xD7)	378,31
C₃².₂(C₃×D₇) = C₉×D₂₁	φ: C₃×D₇/C₂₁ → C₂ ⊆ Aut C₃²	126	2	C3^2.2(C3xD7)	378,37
C₃².₃(C₃×D₇) = D₇×C₃×C₉	central extension (φ=1)	189		C3^2.3(C3xD7)	378,29

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