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

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

		d	ρ	Label	ID
C₆³		216		C6^3	216,177

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

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₆²)⋊₁C₃ = C₂×C₃²⋊A₄	φ: C₃/C₁ → C₃ ⊆ Aut C₂×C₆²	18	3	(C2xC6^2):1C3	216,107
(C₂×C₆²)⋊₂C₃ = C₂³×He₃	φ: C₃/C₁ → C₃ ⊆ Aut C₂×C₆²	72		(C2xC6^2):2C3	216,115
(C₂×C₆²)⋊₃C₃ = A₄×C₃×C₆	φ: C₃/C₁ → C₃ ⊆ Aut C₂×C₆²	54		(C2xC6^2):3C3	216,173

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

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₆²).₁C₃ = C₆×C₃.A₄	φ: C₃/C₁ → C₃ ⊆ Aut C₂×C₆²	54		(C2xC6^2).1C3	216,105
(C₂×C₆²).₂C₃ = C₂×C₃².A₄	φ: C₃/C₁ → C₃ ⊆ Aut C₂×C₆²	18	3	(C2xC6^2).2C3	216,106
(C₂×C₆²).₃C₃ = C₂³×3_-¹⁺²	φ: C₃/C₁ → C₃ ⊆ Aut C₂×C₆²	72		(C2xC6^2).3C3	216,116

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