When I'm checking the Google results for our site's
site:example.com, we get lots of index results like
How do I disallow this type URL, so they don't show up in the search results?
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This is definitely the case when you should use meta tag "robots" and "noindex" the subdomain or what ever pages you want to hide from serps. After that, you could consider using url removal tool from google and getting rid of pages you don't want to see in serps, which will speed up the process a bit.
Do not go with robots.txt and blocking content of this type.