When I was at Google my entire management chain had the title "software engineer" (except Alan Eustace, who officially had the title "VP of engineering" but had a hardware engineering background, and Larry Page, who had the official title of "CEO"). That was 6 levels up, including me. Amit Singhal (who was 3 levels above me and responsible for a department of 2000 people or so) was still titled "software engineer".