If it was com.something you have to type the com first. If "something" is first, you by the time you get to "som" it will probably have something.com in the dropdown list.
I would say its easiest if the most variable part is first, not only for autofill but for the way I think about it.
When you talk about "most significant" you mean the "largest" category. To me the actual most significant is the part that identifies the most unique thing you are typing in, and that tends to be the domain.
Modern web browsers will complete from any start position in an URL (and some also from the title of the document, I think). E.g. if I have visited the Wikipedia article on irish setters and I start typing irish, it will suggest that article. In the same fashion, if the URL was com.example and you typed exa, it should suggest com.example.
I would say its easiest if the most variable part is first, not only for autofill but for the way I think about it.
When you talk about "most significant" you mean the "largest" category. To me the actual most significant is the part that identifies the most unique thing you are typing in, and that tends to be the domain.