I agree with you Nicole.
In my opinion "the six main groups" gives more detail about the "maximum" you are talking about. And the verb "is" refers to the "maximum".

Do I understand correctly that there are at most those six groups, and that there may be less than six ?

Then you could suggest to your pal to use at most...

Else, I'd prefer "there is a maximum of", too.

Thanks for the comments.
Just to clarify: it's not an "at most" situation, there are 6 groups and they are all used. And I know, in that case, why not just say "there are six main groups" and be done with it. But we need to emphasize that there can't be more than 6 main groups. We used to use a lot more than that, and now this document is explaining that the whole big list has been reduced to just six groups, so don't use any more than that.

You said: There are six groups and they are all used. There cannot be more.

That, to me, sounds like "there are EXACTLY six main groups."

The maximum of six groups has (already) been reached.

Maybe that could be an option?

You can say "There are a maximum of six main groups." First, consider the sentence "There are six main groups"; then ask yourself how you might qualify the word "six", as follows:

There are at most six ... (as discussed)
There are precisely six ...
There are about six ...
There are no more than six ...

Looking at it this way, you can consider the phrase "a maximum of" as being a qualifer on the word six, and thus, to my mind at least, "There are a maximum of six ..." is a perfectly reasonable construction.

It is really a matter of perspective. I would avoid the construction altogether and go for something less ambiguous.
I have the impression that in is/are discussions most BE speakers go for "are" when a lot of AE speakers go for "is".

I've noticed the BE/AE difference on plurals too, in things like "the company is/are", "the team is/are", etc. Maybe that accounts for some of the differing opinions here.

I went with "is", because that was my first instinct as an AE speaker. I could have rewritten it to be "there are exactly six main groups" or something like that, but I was trying not to rewrite too much in the file. Besides, it's only a document that will be used internally by a small group people, and they're not the types who will trouble themselves too much about grammar. I just wanted to make sure if I changed it to "There is" based on my feel for the langugage, I wouldn't be adding a mistake.

Thanks for all the help everyone!

This is one of those things it's hard to think about without confusing yourself, but I don't think it's an AE/BE thing at all, and I definitely agree with Joe W that 'are' isn't necessarily wrong. It depends on which idea you want to express; I still can't quite tell from your description.

There is a maximum of six groups = There is a limit of six groups. The cutoff number is defined as six groups.
= We're currently accepting applications from groups. No more than six (hypothetical) groups can participate.
(general rule, not a description of any particular existing groups)

There are a maximum of six groups. = There are at most six groups. There are six groups at a maximum.
= We've done a rough count of the (real) groups that are likely to attend. We're sure there won't be more than six of them.
(specific description, not a general rule)