A high-resolution measurement of fragment-fragment-γ triple coincidence events in the symmetric and near-symmetric mass exit channels from the 28Si+28Si reaction has been undertaken using the EUROGAM Phase II γ-ray spectrometer. The bombarding energy of Elab(28Si)=111.6 MeV has been selected to populate the conjectured Jπ=38+ quasimolecular resonance in the 56Ni dinuclear system. In the 28Si+28Si symmetric mass exit channel, the resonance behavior is clearly verified at the chosen energy. The population of highly excited states in the 24Mg, 28Si, and 32S nuclei is discussed within a statistical fusion-fission model. Evidence is presented for selective population of states in the 28Si fragments arising from the symmetric fission of the 56Ni compound nucleus. The enhanced population of the Kπ=3-1 band of the 28Si nucleus, indicative of an oblate deformed shape, suggests that the oblate configuration plays a significant role in the resonant process. Fragment angular distributions for the elastic and low-lying inelastic channels as well as γ-ray angular correlations for the mutual inelastic channel (2+,2+) indicate that the spin orientations of the outgoing fragments are perpendicular to the orbital angular momentum. This unexpected result, which is different from the alignment found for the resonance structures in the 24Mg+24Mg and 12C +12C systems, suggests a situation where two oblate 28Si nuclei interact in an equator-to-equator stable molecular configuration. A discussion concerning the spin alignment and spin disalignment for different reactions such as 12C +12C, 24Mg+24Mg, and 28Si+28Si is presented.