AbstractThis study compares various multigrid strategies for the fast solution of elliptic equations discretized by the hybrid high‐order method. Combinations of ‐, ‐, and ‐coarsening strategies are considered, combined with diverse intergrid transfer operators. Comparisons are made experimentally on 2D and 3D test cases, with structured and unstructured meshes, and with nested and non‐nested hierarchies. Advantages and drawbacks of each strategy are discussed for each case to establish simplified guidelines for the optimization of the time to solution.