There are 88 constellations which are named for mythological beings. A constellation is a groups of stars in the sky. Some constellations resemble the animals or people they are named for and others were merely named in honor of those figures. Read more: enchantedlearning.com/subjects/astronomy/stars/constellations.shtml.
The constellations are not in the solar system, they are in the galaxy. And there can be as many as you like, as they are arbitrary defined. The IAU defined 88 constellations, but that's just a convention.