David Drummond speaks during a meeting of the Advisory Council to Google on the Right to be Forgotten in Paris.

Alphabet's board of directors has opened an investigation into how executives handled claims of sexual harassment and other misconduct, including behavior of Chief Legal Officer David Drummond, who has been accused of having relationships with employees.

The board has formed an independent subcommittee to look into the issues and has hired a law firm to assist with the investigation, according to materials viewed by CNBC.

An Alphabet spokesperson said, "As has already been confirmed in public court filings, in early 2019, Alphabet's Board of Directors formed a special litigation committee to consider claims made by shareholders in various lawsuits relating to past workplace conduct."

Alphabet shareholders sued the board in January for allegedly covering up sexual misconduct from executives, including former Android co-founder Andy Rubin. The company let go of Rubin and paid him $90 million after an internal investigation found sexual assault claims credible, according to a report in the New York Times. Rubin denied any wrongdoing in statements at the time of the report. The report of Rubin's payout set off a company-wide walkout by employees last November.

In August, former Google legal employee Jennifer Blakely wrote a lengthy Medium post that said she and Drummond started dating in 2004 and later had a son together. Drummond was married to somebody else at the time. Blakely said Drummond later refused to discuss child support, calling his behavior "nothing short of abuse." She also claimed he had affairs with other people at the company.

The company has been silent on the issue, only pointing to a short statement Drummond made, which denied the claims. "Other than Jennifer, I never started a relationship with anyone else who was working at Google or Alphabet. Any suggestion otherwise is simply untrue."

CNBC previously reported that Drummond dated a 37-year-old Google employee, Corinne Dixon, whom he then married over Labor Day weekend. Dixon was not in Drummond's chain of command.

Drummond this week sold $27 million worth of shares, according to materials from the Securities and Exchange Commission. The company paid him $47 million last year, making him one of the highest paid execs.

He joined Google in 2002 after serving as the company's first outside counsel, and served as chief legal officer and vice president of corporate development until 2015, when he became chief legal officer and SVP for parent company Alphabet. During his tenure, Drummond has also led global teams in charge of public policy, mergers and acquisitions, public relations and communications, and has held senior roles within Alphabet's investment arms GV (formerly Google Ventures) and Capital G.

Correction: This story has been updated to correct Corinne Dixon's age. She is 37.

WATCH NOW: Google employees walk out to protest the handling of sexual harassment.