Full time management or specialized jobs take a while in any company, but I'm sure you know that. I work in management in my full time job (another Fortune 500) and we sometimes take up to 4 months to actually complete a hiring process for management or technical positions.
I'm assuming this job was open and you were interviewed for an actively open position, yes? Usually, if there were other applicants and you simply lost the position, you would be notified. So hopefully, the job is open, and you are still in the running. I'd ping the HR person on a weekly basis via email and/or telephone just to keep your finger on the pulse.
Good luck.