How to create multiple TYPES of objects from one menu?

Question

Q: How can I create a single class to create objects of multiple 'object classes' in a way that is not a huge switch statement?
Explaination:
Let's say that I have an application that I am building, that manages five hundred object types. A properly-built object subclassing tree is created, and I want to be able to create objects of any 'leaf node' of this subclassing tree using a single 'objectCreate()' method in a 'factory object'. The purpos of this method will be to create an instance of the correct object, pass a handle to a few collections for properly sorting and storing these objects in groups.
Usually, one could create a switch in this function, testing for the type of object that the user wants to create from the menu. But in the case of having hundreds of possible object choices, this becomes harder and harder code to maintain (let alone performance).
Any suggestions?

Answer 1

But if my menu has:
1. German Shepard
2. Doberman Pinscher
3. Malamut
4. Persian Long-hair
5. Siamese
6. Tabby
And my object class tree goes:
                              [ Animal ]
             [ Cat ]                              [ Dog ]
  [ various breeds ]                         [ various breeds ]How do I code the menu class to respond to the input, so that it runs the correct [breed] object's constructor?
The line:
Animal choice = new xxxxxxxx();
I can't use a variable to replace 'xxxxxxxx' in run-time, but having a ton of choices in code sounds/looks unreasonable.
if (choice == "Doberman Pinscher")
Animal choice = new doberman();
else if (choice == "Tabby")
Animal choice = new tabby();
Do you see what I am trying to avoid? I am not experienced enough to instantly realize how to avoid the latter, and instead, do a single instantiation command for the correct constructor.