According to Clinical Anatomy For Dummies, there are a total of 18 intrinsic muscles that work to move each hand. These muscles are in three groups: the thenar muscles, the hypothenar muscles and the interosseous muscles and the lumbricals.
The four thenar muscles work to move the thumb and the inside of the hand. The hypothenar muscles work together to move the pinky finger and the outside of the hand. Finally, the interosseous muscles and the lumbricals work to move all of the fingers and the palmar region of the hand. These muscles are all intertwined and work together to extend and flex each finger.