If the page seems to load forever, it mostly means that your blog produces a notice or warning that isn't visible, but that disturbs the data transfer. Try to find out what that message says and fix the reason.
There are 3 possibilities that you can try:
1. Find the conflicting plugin
Deactivate all other plugins and switch to a WordPress default theme. Then reload the Tag Groups page. If it works now, reactivate all other plugins again, one by one. Every time try again the Tag Groups page. If it stops working after you activate a plugin, then this one is causing a conflict. (There might be more than one.)
2. Check the Browser Console
Now, with the console open, reload that page. In the console check the "error" and the "log" tabs. If you find errors, warnings or notices, they often contain a hint about the plugin or theme that causes an error.
3. Display messages in the Debug.log
In your wp-config.php file, set:
define( 'WP_DEBUG', true );
define( 'WP_DEBUG_LOG', true );
then reload the page that caused the problem and check the debug.log file inside the /wp-content/ directory for messages that occurred while loading the page.
Some messages can give you a hint about what causes the error. It could be a part of the code that is not compatible with your server configuration or your version of WordPress, or a plugin simply needs an update or needs to be fixed by its author.