How can I have the option on my form to Create or Join an existing group?

I would like people when they register, to create or join a group. Once I group is created, I would like people registering to see the already existing groups. Further, once a group is created, I would like people to be able to pick a group to join. 

To my understanding, you would like your respondents to create a group and this would mean they would have to fill up one of your forms to create one, is that correct? Then, you would like the details of the group that was previously created to be available for other new respondents to see (especially the "Group Name", I guess).

I would like to apologize, I'm afraid it would not be possible. There is no way we can pull out submission data and use it or import it to become options in a dropdown field(or other form fields) within Jotform. This may require you to do a bit of programming (and I suggest you hire a developer as necessary) but you may also try using the full source code of your form to set this up to meet your requirements.

https://www.jotform.com/help/104-How-to-get-the-Full-Source-Code-of-your-Form