Enable group submissions by navigating to Customize -> Subgroups -> and select the option to turn on group submissions. Once here, choose Enabled -> Shareable Link. Copy this link.
Give this link to the groups that should be subgroups. They will then log in and submit their group to be part of your Network. The primary organizer will receive an email asking them to approve the subgroup submission. Note: You can also go to Manage Subgroups and search for any group that is not yet approved and approve them there (filter by the ones not approved).
Delete the affiliations. You can remove them as an affiliate after they become a subgroup (or beforehand if you prefer) by going to manage affiliations.
Finally, you'll want to go to manage subgroups and on the "Actions" column, choose the "move" action for that subgroup if you want to place it somewhere specific in the network.
Converting a subgroup to be an affiliate
Go to Network -> Manage Subgroups, find the group you want to remove from this affiliate list
Go to Network -> Manage Affiliates and click "Add New Affiliate" - search and add
The Affiliate will need to verify and approve the affiliation.