A statistical analysis of the available literature data and data obtained in this work on the wave numbers of the lines that appear in triplet-triplet rovibronic transitions of the H₂ molecule was performed. This allowed us to verify and refine the controversial identification of spectral lines and find the optimum rovibronic level energy values for the c³II± _u, and s³ Δ ^-_g states. The ratios between the line strengths of the P, Q, and R branches of the (4dπ) r s³ Δ ^-_g, s³ Δ ^-_g → (4d?) s(2pδ) c band systems of the H ₂ molecule were measured systematically. The calculation results obtained in the Frank-Condon approximation differed substantially (by up to two orders of magnitude) from the experimental data. The dependences of the ratios between rovibronic line strengths of the r c and s c transitions on the rotational quantum number N' of the upper level were found to correlate with each other. The deviations of adiabatic theory increase as N' grows, which is evidence of an important role played by electronic-rotational interactions in the perturbation of transition probabilities. The experimental ratios between the probabilities of rovibronic transitions satisfactorily agree with the results of calculations within the framework of the simple nonadiabatic model taking into account electronic-rotational interaction of radiating adiabatic states in the approximation of pure precession. The dependences of transition probabilities on N' were obtained for the first time for the first four diagonal bands of the r³ II ^-_g s³ Δ ^-_g → →, c³II±_u transitions.