Final answer:
Proteus vulgaris, a rod-shaped chemoheterotroph, is classified with the Proteobacteria, specifically within the Gammaproteobacteria class.
Step-by-step explanation:
The chemoheterotroph Proteus vulgaris is a rod-shaped bacterium classified with Proteobacteria. This classification is supported by the fact that Proteobacteria is a phylum of gram-negative bacteria which includes a broad range of bacteria, some of which are part of the normal human microbiota as well as many pathogens. It is subdivided into five classes, including Alphaproteobacteria, Betaproteobacteria, Gammaproteobacteria, Deltaproteobacteria, and Epsilonproteobacteria.
Proteus vulgaris falls under the Gammaproteobacteria class, which consists of a variety of genera that are known for their diverse metabolic capabilities and habitats. Gram-negative nonproteobacteria include different taxa such as Chlamydia, spirochetes, Cytophaga, Fusobacterium, Bacteroides group, Planctomycetes, and phototrophic bacteria. However, since Proteus vulgaris is not an intracellular pathogen, not a spiral bacterium, and not known for phototrophic capabilities, it is not classified with Chlamydia, spirochetes, or the phototrophic bacteria.