Multiple groups of what? The question is vague, almost to the point of incomprehensibility.

Here's a model for you: Gmail. Gmail allows users to tag content (i.e., emails) with zero or more labels, and displays a list of labels. When the list gets too long, the user can decide which are always visible, and which are hidden by default. Clicking on a label shows all of the content tagged with that label.

Simultaneously, a built-in search feature allows users to find content by free-text searching (which is orthogonal to labels.)