The 165th Infantry (Regiment) - the 69th New York Infantry prior to 1917 - was an element of the 42d "Rainbow" Division during World War I. The regiment was assigned to the 27th Infantry Division in the Pacific during World War II (the 42d "Rainbow" Division served in the European Theater of Operations).
This may seem trivial but many - if not most - of those seeking information here are almost completely ignorant of military history, traditions and organization and are confused to begin with. To post incorrect information merely adds to the confusion.
You might try:
27th Infantry Division Assn. 215 Lincoln Ave. Troy, NY12180 (518)272-5585
You might inquire as to whether there is also a Regimental Association (165th Infantry).