Keeping owners in a folder copy

I'm trying to copy a folder (SRC) containing some files and subfolders. The content and SRC itself have setgid bit enabled (that is the s in place of the x in the group triplet). Furthermore, the group of the whole content is srcgrp while the files have different owners (let's say me, she and they). Now, I want to copy all the folder (SRC included) into another folder (let's say /mnt/d/SRC to /home/dog/data/SRC). The problem is as follows: when I prompt cp -Rp /mnt/d/SRC /home/dog/data/SRC the folder is being copied in /home/dog/data/SRC but the owner of all the contents become me, even if I give chmod g-s /home/dog/data previously. I'd like to keep the owners of source files. How could I get it? Thank you.