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The company behind Navi, the Internet protocols (including Protocol 7), and other such technologies. It was they who fired Eiri Masami for his modifications to Protocol 7, and they who hired the Men in Black to get rid of Knights and find out exactly what Lain is.
Tachibana is apparently afraid of what Eiri did, and as a giant IBM/Microsoft company, they should! With no devices needed for Wired communication, they'd be out of business! They've taken to opposite view of Eiri: Reality is more "real" than the Wired, but not because this would help humanity in the long run, they believe this because stopping Eiri would keep them in business.