Autofac - resolving component with parameters dynamically

I have a class that takes an interface as a constructor argument. There are two implementations of this interface and I want to decide what implementation to use at runtime based on a variable.

The problem is that the class above is deep in an object heirarchy that is resolved by Autofac and so I can't pass in the argument.

Somehing like below is what I am trying to achieve.

public interface IInterface1 {}
public interface IInterface2 {}

public class Class1 : IInterface2
{
    public Class1(IInterface1 interface1)
    {
    }
}

public class Class2
{
    public Class2(IInterface2 interface2)
    {
    }
}

public class Class3
{
    public void GetClass2Instance(string interface1ImplementationToChoose)
    {
        // want to change which implementation of IInterface1 is resolved based on the interface1ImplementationToChoose variable
        var class2 = container.Resolve<Class2>();
    }
}

Any ideas?

UPDATE:

To clarify, this is an existing object hierarchy that is used by existing applications that work fine. Also, the object model is much larger than the one shown in this example. As a result I don't really want to have to pass down a factory to each constructor in the object graph to be used by a class deep in that graph.

Is there a way of getting a different implementation of IInterface1 passed into Class1 without Class2 knowing anything about it?

Thanks