From my time reading blogs such as Information Dissemination, USNI, Neptunus Lex, and CDR Salamander (for example), it does seem like the people most likely to be promoted to Rear Admiral to command a CSG are usually aviators. There is a lot of criticism that not enough people from subs and 'phibs are selected for flag rank, and that is leading to a lack of diversity of thought in naval strategy. Perhaps the criticism is a sign this could be changing.
The navy posts
bios of its COs and admirals. You might want to browse them and see what paths got them where they are today.