There are 6 relay teams, each with 4 members, competing for gold, silver and bronze medals in an Olympic final. If each team has an equal chance of standing on any given podium, how many different arrangements of the competitors are possible?

Note: All 6 teams can finish 1st, 2nd or 3rd. Each member of a winning team can stand in any order on the podium, but obviously members of one team will not stand on another team's podium