Extensions 1→N→G→Q→1 with N=C₃ and Q=C₆.₆S₄

Direct product G=N×Q with N=C₃ and Q=C₆.₆S₄

		d	ρ	Label	ID
C₃×C₆.₆S₄		48	4	C3xC6.6S4	432,617

Semidirect products G=N:Q with N=C₃ and Q=C₆.₆S₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(C₆.₆S₄) = C₃²⋊₅GL₂(𝔽₃)	φ: C₆.₆S₄/C₃×SL₂(𝔽₃) → C₂ ⊆ Aut C₃	72		C3:(C6.6S4)	432,620

Non-split extensions G=N.Q with N=C₃ and Q=C₆.₆S₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₆.₆S₄) = C₁₈.₆S₄	φ: C₆.₆S₄/C₃×SL₂(𝔽₃) → C₂ ⊆ Aut C₃	72	4+	C3.1(C6.6S4)	432,253
C₃.₂(C₆.₆S₄) = C₃².₃GL₂(𝔽₃)	φ: C₆.₆S₄/C₃×SL₂(𝔽₃) → C₂ ⊆ Aut C₃	216		C3.2(C6.6S4)	432,256
C₃.₃(C₆.₆S₄) = C₃²⋊₃GL₂(𝔽₃)	central stem extension (φ=1)	72	6	C3.3(C6.6S4)	432,258

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Extensions 1→N→G→Q→1 with N=C3 and Q=C6.6S4