Subscription (write) to groups - Ask permission by form?

Hello! I'm a newby in joomla and in CB. I'm planning to make an italian art community with hierarchical groups. For example a root parent "painting" group and various subgroups :oil, acrilic, watercolor...etc, and other parent groups like sculpture, photographers, architecture....etc... I prefer that every group be public (only for reading) for guest (subscribed) of my web site but i need that they must ask a permission to partecipate and write posts/comments in the group they choose. I would like a process similar to facebook where you have to compile a form and then admins of the group can acept or refuse the request.
Thank you for your help and greetings from italy.
 

CB GroupJive should be able to provide that. You'd use Categories for the parent groups, but these are just categorization and don't have any interactions. Groups themselves can be Public and the only people that can interact with a group (e.g. post on the activity stream, upload photos, etc..) are members of that group, but you can require group moderators/admins/owner to approve join requests to the group to satisfy your approval process by setting the group type to Approval.

I recommend giving it a try on our demo site below. There's several views available as well for finding groups.

All Groups:  demo.cbdemosites.com/community/groups/allgroups
Group Category:  demo.cbdemosites.com/community/groups/1-community-builder-add-ons
Group Categories:  demo.cbdemosites.com/demos/cb-groupjive/all-categories/allcategories

Thank you very much for your help. Can i make parent groups and child subgroups or only categories and groups? I think i can do it with CB builder but i'm not sure. For example a parent painting group and oil,acrilic,watercolor....like child groups. Thanks, Grazie e saluti dall' Italia

There is no subgrouping functionality in CB GroupJive just a Category > Group structure. You could just prefix categories though for example.

Category: Painting - Oil
Category: Painting - Acrylic
Category: Painting - Watercolor

Then you'd have user groups within those categories. If groups are not going to be managed or created by users, but by you as the administrator you could do the following.

Category: Painting
- Group: Oil
- Group: Acrylic
- Group: Watercolor

Then set all 3 groups types to Approval so users trying to join the group require approval. The contents of the group will be public though as you're wanting.