Searching fields in Group module
I found an answer to my question. Its all in the view settings.

First, I changed the format from unsorted list of items/groups to Geolocation - CommonMap and modified its settings. This is to display all groups in a single map(A simple solution that I should have noticed at first).

Second, I added all fields needed to be displayed in a group in the map.

Lastly, I added desired filter(this is to search for a group).