(I was nerdy enough to read all the ITS stuff recently).
There two different things to do but it matters whether you have a secondary or non-personal society account. In my experience, normal students don't know what type they have by name, so I'll describe each.
If your society's e-mail account is a "secondary account"-- it's tied to your personal account like it used to be in the old days, where your personal account and the society account had the same password and you were told to never ever ever share your society e-mail account password, you will have had to at one time go on to Telnet to except ownership of this type of account so if you've never heard of Telnet, you probably have the other type: with this type you should change your personal password and about an hour later or so your society e-mail account will switch over by itself.
If your society's e-mail account is a "non-personal account"-- if you created the account within the past year or if you had problems with the account and were told by ITS that they had created you the non-peronal type, if you've never heard of things called PINE or Telnet (secondary accounts would have made you come into contact with those at least once in your life), especially if you went online and filled out an online form on the ITS website to get the account set up (as opposed to came in person to the Student Union or sent doserv an e-mail, which is what people used to do), if you were told that it's okay to share your password with anyone that the society felt needed access to the account even though you owned the account because the society's non-personal e-mail account's password should not be the same as your personal account: with this type you have to change both your personal account password and change your society's account password and then retell those society people the new password. Just changing your own password will still have your society e-mail account in risk and if someone were to do nasty things with your society account, you'd get blamed because you're the owner who didn't change the password like you were supposed to!
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I love cheese.