Part of cigarette lighter connection stuck

When I removed the Magellan from the lighter connection, part of the end of the Magellan stayed in the hole, and it fits so tightly, I need to know how to get it out.

There is a "screw" connection on the line from the GPS to the lighter. I wonder if I am missing a small piece in the connection set up.

I don't know if there is another piece between the two that may have fallen out.

Help!