can other people on facebook see what groups im in?

[pri✍]

Only your secret group doesn't reveal to other people; your open & close group can be easily found out.

Thus said, if you want to join open & close group, use FB account not in your own name, just make one for that purpose. To make other account, as it's formally prohibited, do not use same email address or phone number; even many has more than one, but if Facebook caught you, you risk your all your account to be banned.