acidithiobacillales acidithiobacillales the acidithiobacillales are an order of bacteria within the class acidithiobacillia and comprises the genera acidithiobacillus and thermithiobacillus. originally, both were included in the genus thiobacillus, but they are not related to the type species, which belongs to the betaproteobacteria. acidithiobacillales acidithiobacillus ferrooxidans scientific classification domain: bacteria phylum: pseudomonadota class: acidithiobacillia order: acidithiobacillalesgarrity, bell & lilburn 2005 families & genera acidithiobacillaceae acidithiobacillus thermithiobacillaceae thermithiobacillus