We present single-photon spectroscopy in molecular hydrogen starting from the metastable c(3)Pi(u)(-) state to a number of triplet nd-Rydberg states (v=0-4, n=12-20). Using fast beam spectroscopy both the autoionization channel and the predissociation channel are quantified, field free, as well as with small electric fields. Coupling with the i(3)Pi(g) state is assumed to be responsible for field-free predissociation of the v=0 Rydberg levels. The stronger observed predissociation channel of the v=1 Rydberg levels is due to the nonadiabatic interaction with the h(3)Sigma(g)(+) state in combination with l mixing due to an external electric field. No direct evidence is found for possible electric field induced predissociation of the gerade Rydberg states by low lying ungerade states. The competition between autoionization and predissociation is discussed in terms of possible consequences for dissociative recombination involving low energy electron collisions with the H-2(+) molecular ion. (C) 2004 American Institute of Physics.