There are five main branches of chemistry, and then there are many subdivisions of chemistry into specialized fields.
The five main branches are inorganic chemistry, organic chemistry, analytical chemistry, physical chemistry, and biochemistry.
We discussed biochemistry and organic chemistry already. Inorganic chemistry is usually described as what organic chemistry does not deal with. Analytical chemistry is the study of the properties of matter and tools to discover those properties. Physical chemistry applies physics to the study of chemistry, including thermodynamics and quantum mechanics.
Sub-branches of chemistry include astrochemistry (the chemistry in stars and interstellar gas and dust), electrochemistry (what happens when electrical currents flow though chemicals), food chemistry, geochemistry (the study of the composition of the Earth), nuclear chemistry, polymer chemistry, spectroscopy, theoretical chemistry, and many more.