What are the three groups animals can be divided into based on how they get their energy?

You are talking about different elements of the food chain.  Producers (autotrophs) are plants that utilize the power of sunlight to produce their own food.  Decomposers are bacteria, molds, and fungi that feed on decaying matter and help break them back down into base nutrients.  You are talking about the part of the food chain occupied by animals.  Animals are consumers in that they cannot produce their own food and must eat other living things as a source of food.  They can be divided into three basic categories.  Animals that eat only plants (producers) are called herbivores.  Animals that eat other animals (meat) are called carnivores.  And animals that eat both herbivores and carnivores are called omnivores.  Humans are an example of an omnivore (although vegetarians would technically be herbivores).
http://image.slidesharecdn.com/herbivorecarnivoreandomnivoreanimals-131127045245-phpapp01/95/herbivore-carnivore-and-omnivore-animals-2-638.jpg?cb=1385528000