Context. The empirical relations between supermassive black holes and their host spheroids point towards the crucial role of galactic nuclei in affecting the properties of their hosts. A detailed understanding of how the activity of a galactic nucleus regulates the growth of its host is still missing. Aims. To understand the activity and the types of accretion of supermassive black holes in different hosts, it is essential to study the radio-optical properties of a large sample of extragalactic sources. In particular, we aim to study the radio spectral index trends across the optical emission line diagnostic diagrams to search for potential (anti)correlations. Methods. To this goal, we combined flux densities from the radio FIRST survey at 1.4 GHz (with the flux density range 10 mJy ≤ F1.4 ≤ 100 mJy) for 396 SDSS sources at intermediate redshift (0.04 ≤ z ≤ 0.4) with the Effelsberg radiotelescope measurements at 4.85 GHz and 10.45 GHz. The information about the optical emission-line ratios is obtained from the SDSS-DR7 catalogue. Results. Using the Effelsberg data, we were able to infer the two-point radio spectral index distributions for star-forming galaxies, composite galaxies (with a combined contribution to the line emission from the star formation and AGN activity), Seyferts, and low ionization narrow emission region (LINER) galaxies. Conclusions. While studying the distribution of steep, flat, and inverted sources across optical diagnostic diagrams, we found three distinct classes of radio emitters for our sample: (i) sources with a steep radio index, high ionization ratio, and high radio loudness, (ii) sources with a flat radio index, lower ionization ratio, and intermediate radio loudness, (iii) sources with an inverted radio index, low ionization ratio, and low radio loudness. The classes (i), (ii), and (iii) cluster mainly along the transition from Seyfert to LINER sources in the optical diagnostic (Baldwin, Phillips & Telervich; BPT) diagram. We interpret these groups as a result of the recurrent nuclear-jet activity.