Eu₅In₂Sb₆ is a member of a family of orthorhombic nonsymmorphic rare-earth intermetallics that combines large localized magnetic moments and itinerant exchange with a low carrier density and perpendicular glide planes. This may result in special topological crystalline (wallpaper fermion) or axion insulating phases. Recent studies of Eu₅In₂Sb₆ single crystals have revealed colossal negative magnetoresistance and multiple magnetic phase transitions. Here, we clarify this ordering process using neutron scattering, resonant elastic x-ray scattering, muon spin-rotation, and magnetometry. The nonsymmorphic and multisite character of Eu₅In₂Sb₆ results in coplanar noncollinear magnetic structures with an Ising-like net magnetization along the a axis. A reordering transition, attributable to competing ferro- and antiferromagnetic couplings, manifests as the onset of a second commensurate Fourier component. In the absence of spatially resolved probes, the experimental evidence for this low-temperature state can be interpreted either as an unusual double-q structure or in a phase separation scenario. The net magnetization produces variable anisotropic hysteretic effects which also couple to charge transport. The implied potential for functional domain physics and topological transport suggests that this structural family may be a promising platform to implement concepts of topological antiferromagnetic spintronics.