Thanks, your suggestion helped me to solve the problem:
The Java Console showed (among other info):
admin.php?page=Wordfence:27
Failed to load resource: the server responded with a status of 404 (Not Found) http://MYDOMAIN.NL/SUBDIR/wp-content/plugins/wordfence/js/jquery.tmpl.min.js?ver=4.0.3
Uncaught TypeError: Object [object Object] has no method 'tmpl' admin.js?ver=4.0.3:46
I have Wordfence running on some other sites. They didn't have this problem, whe opened within in the same (Chrome or any other) browser.
I found that the file jquery.tmpl.min.js was actually missing in this case. No idea why.
I copied it there from one of the other sites. That fixed it.