Among the ~2157 unassociated sources in the third data release (DR3) of the fourth Fermi catalog, ~1200 were observed with the Neil Gehrels Swift Observatory pointed instruments. These observations yielded 238 high signal-to-noise ratio X-ray sources within the 95% Fermi uncertainty regions. Recently, Kerby+ (2021, J/ApJ/923/75) employed neural networks to find blazar candidates among these 238 X-ray counterparts to the 4FGL unassociated sources and found 112 likely blazar counterpart sources. A complete sample of blazars, along with their subclassification, is a necessary step to help understand the puzzle of the blazar sequence and for the overall completeness of the gamma-ray emitting blazar class in the Fermi catalog. We employed a multi-perceptron neural network classifier to identify flat spectrum radio quasars (FSRQs) and BL Lac objects among these 112 blazar candidates using the gamma-ray, X-ray, UV/optical, and IR properties. This classifier provided probability estimates for each source to be associated with one or the other category, such that Pfsrq represents the probability for a source to be associated with the FSRQ subclass. Using this approach, four FSRQs and 50 BL Lac objects are classified as such with >99% confidence, while the remaining 58 blazars could not be unambiguously classified as either BL Lac objects or FSRQs.