SAN FRANCISCO — As a crisis unfurled at Google over an employee memo that argued biological factors helped explain the shortage of female engineers and leaders in Silicon Valley, some of the most pointed critiques of the company’s handing of the issue were posted to its own message boards.

Memegen, an internal forum that uses images overlaid with funny captions, was filled with irreverent posts that openly mocked how an email discussing the memo from Sundar Pichai, Google’s chief executive, had leaked to the media so quickly. Other posts, seen in screenshots of Memegen that were shared with The New York Times by a Google employee, questioned why Google seemed to be taking cues from outsiders.

Memegen is one of many outlets provided by Google to allow employees to express themselves, argue, criticize products or policies, and even protest decisions by management.

Google’s liberal stance toward self-expression, enabled by those online forums, was created in part to show that it is not bound by the conventions that stifle more stodgy companies.