Consider the space of embedded minimal hypersurfaces in a closed Riemannian n-manifold, with the C^k topology. For n=3, a celebrated work of Choi--Schoen gives natural geometric conditions that determine compact subsets of this space; notable extensions to n<=7 were given by Sharp and Ambrozio-Carlotto-Sharp. I will discuss a compactness result for minimal hypersurfaces that are invariant under isometric group actions whose orbit space is smooth and 2-dimensional, which does not require volume or index bounds, nor restrictions on the ambient dimension n. This talk is based on joint work in progress with Dario Corona, Fabio Giannoni, and Paolo Piccione.