Maximum number of Save Group

I'm not aware of such limit.

I have not seen any mention of it in the admin guide. However I currently have over 20 clients in many of my Groups with high parallelism without any problem.

There is no defined limit but could depend on your parallelism, backup window & backup policies preference.

There is no maximum. Realistically though, there would be a maximum number of groups and/or clients that your backup server will be able to manage both as a result of parallelism and how much your backup environment can realistically back up.
Some sensible rules of thumb with groups - start one group at a time, space groups out regularly (10/15 minutes or more), add a manageable number of clients to a group which will not exceed parallelism. An average environment will probably have somewhere in the region of 25-50 groups with up to 10 clients per group.