I would categorise it as a separate department, although it is part of corporate law more broadly (as opposed to family or criminal law, for example)!
Antitrust primarily consists of three areas - antitrust litigation, antitrust regulatory/advisory and merger control (which involves approving mergers and acquisitions by ensuring that the new combined company will not be monopolistic). Merger control is the only area which may be considered 'part of corporate' and if a commercial firm does not do the other areas of antitrust then it is likely that their antitrust team is a support team to the corporate lawyers. That does still not necessarily make it part of corporate although it could be looked at that way, if you were also to consider a tax support department 'part of corporate'.
On the other hand, I know of some firms which include antitrust/competition under their disputes practice. Antitrust litigation is a beast of its own and the lawyers involved in it will often be incredibly specialised even beyond other litigators. Many firms will not do antitrust litigation but antitrust regulatory is more common as clients often seek advice on potential antitrust issues when seeking to enter new markets or develop a new product etc.
I hope that is useful