Trademark infringement by creating a "secret group" on facebook...?

[Mike]

For years I have had a "secret group" on facebook where everyone (apart from management) who has or does work there is a member in it. The secret group name is the same name as my company and now they are telling me I have breached trademark infringement even though i have not created a page, merely a group. I dont think they understand the difference between pages and groups and i believe they think my secret group can be made public somehow...