As mentioned in "How do I import svn branches rooted in different directories into git using git-svn?", you need to grab all the nested branch during the initial import:
[svn-remote "svn"]
url = svn://svnserver/repo
fetch = trunk:refs/remotes/trunk
branches = branches/*/*:refs/remotes/*
tags = tags/*:refs/remotes/tags/*
That is also described in this thread.
For even more complex SVN branch layout (like branches within trunk!), a modification of the SVN repo might be in order first, before putting in place a git-svn integration.
Since Git1.6, "1.6.x offers deep cloning so that multiple wildcards can be used with the --branches option", as mentioned in "Cloning a Non-Standard Svn Repository with Git-Svn".
git svn clone https://svn.myrepos.com/myproject web-self-serve --trunk=trunk --branches=branches/*/* --prefix=svn/