Absolutely. Groups can be public (any member of the network can see the group and post content) or private (only invited network members can see the group and post content). This option is chosen during the setup process, which can be started by clicking on the "Groups" tab and choosing the "Create a New Group" option.
How many groups can I create on a network?
There are currently no limits. Create away!
Do discussions within a Group Forum appear in the Network Forum?
Nope! Group discussions are contained entirely within that group, and don't appear alongside Network Forum discussions.
Can I send messages to my group's members?
Absolutely! The Group Creator and any Group Administrators can send announcements to all members by using the "Send Message to Group" link on the group's main page.