From AIG Ireland website....
Why choose AIG Ireland limited AIG Ireland limited can provide a wide range of innovative insurance and risk management solutions for individuals and businesses. The company underwrites all classes of non-life insurance and provides cover to many of Ireland's leading companies. AIG Ireland limited is a member company of American International Group Inc. (AIG), one of the world's leading international insurance and financial services organisations and has over 30 years of experience in the Irish market
AIG is one of the leading U.S. based international insurance and financial services organisations. Its member companies write a wide range of commercial, personal and life insurance products through a variety of distribution channels operating in more than 130 countries and jurisdictions throughout the world. AIG's global businesses include financial services and asset management, including aircraft leasing, financial products, trading and market making, consumer finance, institutional, retail and direct investment fund asset management, real estate investment management, and retirement savings products
American International Group, Inc.'s common stock is listed on the New York Stock Exchange, as well as the stock exchanges in Ireland and Tokyo
AIG Ireland Limited, AIG House, Merrion Road, Dublin 4, Ireland | Company Registration Number 53654 | Tax Reference Number 4102742AB
Directors: D Andrews SC (Chairman); S B Hehir FCII (Managing); D A Kent; A Baugh (USA); M W Leahy ACII; M J Rafferty; A M Connaughton; G Owens ACII
AIG Ireland limited is regulated by the Financial Regulator
I could be wrong but I'd suggest the above would lead to a reasonable conclusion that AIG ireland is a wholly owned subsidiary. Your "one umbrella" comment and earlier "parent" comment suggest the same. AIG are not "in liquidation problems" either.