Are we talking Perl or grep or something else here? There are many different regex flavors and the matching strategy would also depend on what infrastructure is available in the tool.

For Perl, something like m%/(\d{4}/\d{1,2}/\d{1,2})/\d+/([^/]+)/([^/]+)$% would get the substrings you request into $3, $2, and $1, respectively.