Extensions 1→N→G→Q→1 with N=C₃ and Q=C₂×C₆²

Direct product G=N×Q with N=C₃ and Q=C₂×C₆²

		d	ρ	Label	ID
C₆³		216		C6^3	216,177

Semidirect products G=N:Q with N=C₃ and Q=C₂×C₆²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(C₂×C₆²) = S₃×C₆²	φ: C₂×C₆²/C₆² → C₂ ⊆ Aut C₃	72		C3:(C2xC6^2)	216,174

Non-split extensions G=N.Q with N=C₃ and Q=C₂×C₆²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₂×C₆²) = C₂³×He₃	central stem extension (φ=1)	72		C3.1(C2xC6^2)	216,115
C₃.₂(C₂×C₆²) = C₂³×3_-¹⁺²	central stem extension (φ=1)	72		C3.2(C2xC6^2)	216,116

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Extensions 1→N→G→Q→1 with N=C3 and Q=C2×C62