You can display a directory of all the groups anywhere on your site using the [wpum_group_directory] shortcode (block coming soon).
This shortcode has some parameters to control what it looks like:
per_page – The number of groups to appear on a page. Pagination is then used for more. Default 10
has_search_form – If there is a search form at the top. Default is true
show_public – If to show public groups. Default is true
show_private – If to show private groups. Default is true
You can also use the WPUM shortcode generator button if using the WordPress classic editor: