Intal's CiviCRM needed some customizations. So I delved into CiviCRM's templating system, which is based on smarty. Most things were pretty easy but it took some more time to figure out how to add the Group overview to the Contact Summary.
In sites/default/civicrm_custom/CRM/Contact/Page/View/Summary.tpl I added to the appropriate spot.
{include file="CRM/Contact/Page/View/GroupContact.tpl"}
In order to keep my customizations separate from the core CiviCRM code I tried adding the following lines to the template.
{php}
require_once 'CRM/Contact/Page/View/GroupContact.php';
CRM_Contact_Page_View_GroupContact::browse();
{/php}
But that did not work unfortunately.
So for now I stick with adding the following lines to CRM_Contact_Page_View_Summary extends CRM_Contact_Page_View::view() in sites/all/modules/civicrm/CRM/Contact/Page/View/Summary.php:
require_once 'CRM/Contact/Page/View/GroupContact.php';
CRM_Contact_Page_View_GroupContact::browse();
There should be a nicer solution that doesn't require hacking core CiviCRM code...