The phrase "a different division of" is correct and usable in written English.
It can be used when referring to a separate or distinct section or unit within a larger organization or system.
Example: "The project will be handled by a different division of the company that specializes in marketing."
Alternatives: "another department of" or "a separate branch of".
Each decision was issued by a different division of the Pennsylvania Supreme Court.
Ironically, just a few days earlier, a different division of Google announced its own full-page app adverts.
She added that Corcoran Group's brokers, who work for a different division of the company, were also barred from the building.
That's because printers are made by a different division of IBM, and apparently no one bothered to link the printer pages to the PC pages.
At the show, Schilling and I walked past the French chocolates of Michel Cluizel and saw a photograph of the white-haired patriarch surrounded by his offspring: four scrawny young adults, each assigned to a different division of the business.
After that, many of them end up becoming trading managers or go to a different division of the bank.
Later he was transferred to another educational institution in Caguas, Puerto Rico, but when he tried to participate in an athletic competition he was denied permission because he was classified in a different division on the records of Puerto Rico's Instruction Department.
He's also proposed freezing four vacancies and transferring two police officer positions to a different division as part of a restructuring of the city's share of the helicopter program.
Nor does the Clause prevent a crime from being tried by a jury from a different division (a subset of a federal judicial district) within the same district in which the crime was committed.
The American League East is a different division than many because of the presence of the Yankees and the biggest market in the Western world that comes with them.
And then, the Internet of the future would look a lot like the free Internet of today — with a slightly different division of the spoils.
