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You are not the billing contact for the account.
Even if you are an account administrator, you might not necessarily have billing rights (which are required for modifying your subscription and billing info). See Understanding User Roles to learn more.
You are part of an offline account.
There are 2 different types of LogMeIn accounts: online and offline. While online accounts are able to manage their plans online, offline accounts require assistance from a LogMeIn representative. If you are sure you are the billing contact for your account but still don't see the options described, then you are likely part of an offline account. See What's the difference between online vs. offline accounts? to learn more.
Your account is expired.
If your account is expired, then you or your billing contact will need to renew it before making any additional changes.