A breakaway group is a group of people who have separated from a larger organization or entity. The term 'breakaway group' can be used to describe a variety of different situations, such as a political party that has split from a larger party, a religious group that has left an established church, or a business that has left a larger corporation. In this case, the crossword solution for the term BREAKAWAY GROUP is SECT, which is a religious denomination or philosophical group that has broken away from a larger organization.