This week's book giveaways are in the Cloud and AI/ML forums. We're giving away four copies each of Cloud Native Patterns and Natural Language Processing and have the authors on-line! See this thread and this one for details.
By "fetch" I assume you mean read all of the decedents from a root of the tree in a single database query?
Or do you just want them read in some fashion? Since your relationship is EAGER (default for a ManyToOne) they will all be read when you read the root, just possibly not a efficiently as you may like. One query will be executed for each Group (unless the Group is already in the cache).
You can use "LEFT JOIN FETCH" in JPQL to join fetch "n" levels in a single query, but "n" will be a fixed number.
Depending on your JPA provider you may also be able to use batch fetching, if you are using EclipseLink you can set @BatchFetch on the parentGroup relationship, then if you read a set of Group objects their parentGroups would be read in a single query instead of n queries, as would the parent's parent's etc.
Some databases support hierarchical queries (such as Oracle's CONNECT BY PRIOR syntax), you could define a hierarchical query to read in the entire hierarchy in a single query. You would need to use a native SQL query for this as this is not defined in JPQL, unless your JPA provider provides this extension. If you are using EclipseLink, hierarchical query support is provided using the ReadAllQuery and Expression API.