To change the group(s) of a conversation, first, you need to open your conversation from your conversation list.
Once you have opened your conversation at the top and in the middle of the page you still see the connected groups to this conversation (see picture above). Click on this to begin changing your groups. Note: you must be the owner of the conversation.
A menu will appear on the right hand side of the page (as seen above). In the same way that you selected your group(s) when creating your conversation, just simply check the box next to the corresponding , and/or uncheck the boxes next to groups you wish to remove. Once finished, remember to click the pink save button at the bottom of this menu.