March 26 (Reuters) - Swiss skincare company Galderma announced on Tuesday the underwriters for the company bought an additional 5.6 million shares from one of its shareholders, Sunshine SwissCo AG (EQT), for 298 million Swiss francs ($329.83 million).

Sunshine SwissCo is a wholly owned subsidiary of the Abu Dhabi Investment Authority (ADIA) and Auba Investment.

The shares were bought at 53 Swiss francs per share - the final price at which the company went public, the Cetaphil maker said in a statement.

Galderma's full exercise of the over-allotment option would make placement volume amount to 2.3 billion francs, making it the biggest IPO in Switzerland. The company had raised 2 billion francs initially.

Following the transaction, the shares available to trade as calculated by the SIX Swiss Exchange are expected to increase from 20.4% to 22.8%, Galderma said.

Galderma went public last week making the cosmetic fillers and medical creams maker worth more than $16 billion.

($1 = 0.9035 Swiss francs) (Reporting by Surbhi Misra and Mrinmay Dey in Bengaluru; Editing by Vijay Kishore)