Succeeding at work even if you're not in the boss' circle

Our manager, who oversees about a dozen employees, took over a year ago. Since then, it's become apparent that there are 4-5 staffers whom she seems to be on very good terms with and supports more than the rest of us. She's put them on special projects and in a few cases, promoted them within a year. They all have one thing in common-- they're all related to someone else at our company, by blood or marriage. The company is large with a few thousand people. Because our city is pretty small, it's the biggest employer. Of course, as a result, there's a good amount of nepotism. This leaves me feeling I'm on the outs and will never be "in." She's very chummy with these people and it does feel like they're more or less elevated over the rest of us. I've been there for a few years and have been thinking it's time to ask for a transfer or just find a new employer and apply elsewhere. Is there really any way to overcome this situation and get promoted? I've never been promoted while the people in the "inner circle" have all been promoted.