We develop a comprehensive Ginzburg-Landau theory describing triple-Q magnetic orders on hexagonal lattices, focusing on $O\left(N\right)$ models with $N=2$ and $N=3$. Through systematic analysis of symmetry-allowed terms in the free energy, we establish complete phase diagrams governed by competing interaction parameters. Our theory reveals distinct magnetic configurations including single-Q, double-Q, and triple-Q states, each characterized by unique symmetry-breaking patterns and collective excitations. The framework provides fundamental insights into complex magnetic orders recently observed in materials such as ${\mathrm{Na}}_2{\mathrm{Co}}_2{\mathrm{TeO}}_6$, where the interplay between geometric frustration and multiple ordering vectors leads to exotic magnetic states. Our results establish clear connections between microscopic interactions, broken symmetries, and experimentally observable properties, offering a powerful tool for understanding and predicting novel magnetic phases in frustrated magnets.

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• Magnetic order
• Magnetic texture
• Magnetism
• Landau-Ginzburg-Devonshire theory