Put factory method in abstract parent class

There are three different types of Shapes: Rectangle, Circle, Triangle

These shapes share some code which is placed in the parent (Shape), and there is one method that is implemented differently across these three shapes: draw()

Based on the input value, one of the three implementations of that method gets called:

abstract class Shape {
    @Autowired
    private Rectangle rectangle;
    @Autowired
    private Circle circle;
    @Autowired
    private Triangle triangle;

    public String drawIt(ShapeEnum shape, String param1, String param2) {
        switch(shape) {
            case ShapeEnum.Rectangle:
                return rectangle.draw();
            case ShapeEnum.Circle:
                return circle.draw();
            case ShapeEnum.Triangle:
                return triangle.draw();
        }
    }
    protected int sharedMethod1() {//....}
    protected int sharedMethod2() { //...}
    protected abstract String draw();
}

@Controller
public class Controller {
    @Autowired
    private Shape shape;

    @RequestMapping(path = "", method = RequestMethod.POST) 
    public String getDrawing(@RequestBody GetShapeRequest shapeRequest) {
        return shape.drawIt(ShapeEnum.valueOf(shapeRequest), shapeRequest.getParam1(), shapeRequest.getParam2());
    }
}

Obviously this doesn't work, because Spring cannot instantiate an abstract class that has three children. I'm wondering how I should implement it then? Is there a way to have one parent at the top deciding which child to call? or should I wire in all three children in the controller? I really don't like this idea because I'm going to add tens of other shapes and I prefer to control the flow in Shape rather in controller.