Yes you can create two new groups from a single group.
Once you have your group you can export it to .csv file, split the file into 2 files then action an update import of contacts on each of those 2 groups, choosing to create a new group as you import.
When doing the update import match some key fields such as First name, Last Name and Email address. Then in the Duplicate Processing section tick Update and then leave Email Address as the unique identifier (if they all have an email address).
If some of your contacts in the group(s) do not have an email address then tick Contact ID as the unique identifier and ensure you match the Contact ID field from your file into InTouch in the top section.