The group of organisms that interbreed successfully is called a species.

Here's why:

* Interbreeding: A species is defined by its members being able to reproduce with each other and produce fertile offspring.

* Successful: This means the offspring are viable and capable of further reproduction, ensuring the continuation of the species.

For example, all dogs belong to the same species, *Canis familiaris*, because they can breed with each other and produce fertile puppies. However, dogs cannot interbreed successfully with wolves, which are a different species (*Canis lupus*).