You have to create specific guidelines and scripts for navboxes to work. For example, I couldn't just use the Tabs template on any wiki and have it work. I could try and copy/paste the code... but it won't always work because each wiki has to be designed for it. Each wiki has its own coding and navboxes that may sometimes require other navboxes or templates to work. There are basic templates that are universal from what I remember, and so you may want to start there.
In the example you showed me with the ToT template you used, for example, it could just be that it can't display the Navbox subgroup, because that in itself is its own template. It's a template within a template. The basic Navbox, however, has no issues.
You can look at the community wikia or reach out to a staff member if you need some help. I designed very basic templates years ago, but Mai has since brushed them up herself and is usually the one of the two of us who does navboxes and more sophisitcated coding. We also had a staff member come in from wikia and reach out and help us by formatting the templates to make them more modern to wikia's new standards.