SOAP should be able to find out what groups a user is a member of

From email
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I'm working on a project and we'd like to more neatly integrate the
application with our JIRA setup. We're attempting to use SOAP calls,
but looking through the API I'm not finding everything we're looking
for. We're trying to retrieve the groups that a user belongs to, but
I can't seem to find something that will retrieve them. Failing that,
I thought of the other approach of matching them via retrieving the
users belonging to each particular group, but I can't find a function
to retrieve all the groups.