Small-angle neutron scattering has been performed on lysozyme solutions at different concentrations, both at the Intense Spallation Impulsed Source (ISIS), Rutherford-Appleton Laboratory) and at Orph\'ee (Laboratoire Leon Brillouin). The results show that, in addition to the large-scale structural properties revealed by light-scattering experiments elsewhere, there is also partial ordering on a molecular scale, with features similar to the large-scale ones, provided a suitable scaling of the spatial length is made. We obtained a careful evaluation of the shape and size of the lysozyme molecule that compares favorably with existing data, and achieved a quantitative description of the intracluster structural properties in terms of a preferred distance among macromolecules. In addition, comparison with results obtained for solutions in different chemical and physical conditions allows for some insight concerning the kinds of interactions responsible for the structure.