I will discuss the properties of domain walls arising from non-Abelian discrete symmetries, which I refer to as non-Abelian domain walls. In particular, I focus on S4​, a widely used group in lepton flavour mixing models. I will discuss how the spontaneous breaking of S4​ leads to distinct vacua preserving either a residual Z2​ or Z3​ symmetry. This results in five types of domain walls, SI, SII, TI, TII, and TII, where the first two separate Z2​ vacua and the latter three separate Z3​ vacua. I will highlight that SI, TI, and TIII may be unstable in certain parameter regions, decaying into stable domain walls. I will also explore how these stable walls can collapse, generating gravitational radiation when explicit symmetry breaking is introduced. Finally, I will discuss how a symmetry-breaking scale around 100 TeV could explain the recent detection of nanohertz gravitational waves by PTA experiments.