Non-Abelian topological charges, characterized by their noncommutative algebra, offer a framework for describing multigap topological phases beyond conventional Abelian invariants. Although higher-order topological phases (HOTPs) host boundary states at corners or hinges, their characterization has largely relied on Abelian invariants such as winding and Chern numbers. Here, we propose a coupled-wire scheme for constructing non-Abelian HOTPs and analyze in detail a two-dimensional model as its minimal realization. The resulting Hamiltonian supports hybridized corner modes, protected by parity-time reversal $\left(\mathcal{PT}\right)$ plus sublattice symmetries, and described by a topological vector that unites a non-Abelian quaternion charge with an Abelian winding number. Corner states emerge only when both invariants are nontrivial, whereas weak topological edge states of non-Abelian origin arise when the quaternion charge is nontrivial, enriching the bulk-edge-corner correspondence. The system further exhibits topological phase transitions of both non-Abelian and Abelian characteristics, providing a unified platform that bridges these two distinct topological classes. Our work thus extends the study of HOTPs into non-Abelian regimes and suggests feasible experimental realizations in synthetic quantum matter.

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• Topological phase transition
• Topological phases of matter
• Topological insulators
• Discrete symmetries in condensed matter
• Tight-binding model