Its own.

Well, NSA employees can read each other's emails, probably. I mean, it wouldn't make much sense to have an email system if your employees couldn't read the emails. Would it?

It's just that the NSA can't read its employees' emails when you ask them to do it in order to respond to a Freedom of Information Act request.

"There's no central method to search an email [sic] at this time with the way our records are set up, unfortunately," the NSA's FOIA officer told reporter Justin Elliott last week, apparently with a straight face. Elliott had asked for emails between NSA employees and National Geographic employees during a particular period (for a reason he explains in the linked report if you care). They called back asking him to specify particular employees (they have about 30,000) because, they said, they are not technically capable of searching their own email in bulk. Not. Technically. Capable. The system is "a little antiquated and archaic," the officer told Elliot.

The NSA's budget is estimated at $8-10 billion, it reportedly intercepts and stores 1.7 billion communications every day, using facilities that consume upwards of 70 megawatts of power, making it the single largest power consumer in the state of Maryland (it uses as much as the entire city of Annapolis), and it has some of the fastest if not the fastest supercomputers in the entire world not even counting the monster it is currently building in Utah. But its employees are still using, what, AOL.com? "You've got classified mail!" Okay then.