The navy has launched an investigation into revelations defence personnel are members of an online racist group that calls for members to fight the ''Muslim infiltration of our country''.

At least 20 personnel are members of the Australian Defence League, which is affiliated with the hardline English Defence League, known for its links to football hooliganism and violent street marches.

It is understood some work in the frontline of Australia's efforts to control the number of asylum seekers coming to Australia by boat.

On its Facebook page, the ADL has called for members to go to Lakemba Park for Australia Day. One member wrote: ''It'll be great fun, bring your baseball bats and cricket bats. There will be a lot of balls to hit.''

The page's administrator cautioned members that ''you do understand that if their [sic] is an issue your public comments on here may become a component of an investigation''.