How to access string properties of an object C#

I would like to access to all string properties of an object that has defined classes which also have string properties to apply a certain treatment. For example :

public class Class1 
{ 
   public string String1 {get; set;}
   public Class2 class2 {get; set;}
}

public class Class2 
{ 
   public string String2 {get; set;}
}

Here, I would like to have a property list which contains String1 and String2

For the moment I know how to access to String1 :

var instanceOfClass1 =  new Class1();
var stringsList = instanceOfClass1.GetType().GetProperties().Where(prop => prop.PropertyType == typeof(string))

But this won't access to String2.

Thank you in advance if you have any idea.