The issue has come to light after an unnamed Facebook user reported some hate speech on the website and was subsequently assured that the incident would be investigated.
A Facebook spokesperson said at the time: "We removed both the group and all its posts, including the one you reported."
But, as it transpired, none of that happened.
Instead, the content remained online - and Facebook has now pledged to take action.
The company told the BBC: "We are investigating this issue, and will share more information as soon as we can."
The incident has come to light shortly after Facebook was accused of allowing employers to target job ads based on gender.
The allegation about the practice has been made by the American Civil Liberties Union, which has taken its complaint to the US Equal Employment Opportunity Commission.
But in response to the allegation, Joe Osborne, a spokesperson for the company, explained: "There is no place for discrimination on Facebook.
"It's strictly prohibited in our policies, and over the past year, we've strengthened our systems to further protect against misuse."