Divacancies near or at lattice defects in SiC, the PL5-PL7 photoluminescence centers, are known to have more favorable optical and spin properties for applications in quantum technology compared to the usual divacancies. These centers were previously predicted to be diva-cancies near stacking faults. Using electron paramagnetic resonance, we observe PL5, PL6, and four other divacancy-like centers, labeled PLa-PLd, in electron-irradiated high-purity semi-insulating (HPSI) 4H-SiC. From the observed fine-structure D-tensors, we show that these centers including PL6, which has so far been believed to be an axial center, all have C-1h symmetry. Among these, PLa, PLc, and PLd are basal divacancies and PL5 and PL6 are slightly deviated from axial symmetry, while PLb is different from others with the principal D-zz axis of the D-tensor aligning at similar to 34 degrees off the c-axis. We show that these modified divacancies are only detected in one type of HPSI materials but not in commercial n- and p-type substrates or n-type pure epitaxial layers irradiated by electrons regardless of surface treatments which are known to create stacking faults.