LONDON — Norwegian Cruise Line Holdings, the cruise line operator whose owners include Apollo Global Management, filed for an initial public offering in the United States that may raise as much as $424 million.

The company is offering 23.5 million shares at $16 to $18 each, a regulatory filing Tuesday shows. The midpoint of the range values the Miami-based company at $3.41 billion, or more than 20 times earnings in the 12 months through Sept. 30.