those manufacturing small arms are classified in SIC 3484: Small Arms.
those manufacturing small arms ammunition are classified in SIC 3482: Small Arms Ammunition
Manufacturers. Finding out would take anywhere from a few days to a few years depending on how much money you have.
BRNO ARMS
There are many manufacturers that are members of SAMMI (Sporting Arms and Ammunition Manufactures Institute) including Glock, Hornady, Nosler, and Savage Arms.
The Sporting Arms and Ammunition Manufacturers Institute (SAAMI), sets voluntary national standards for ammunition and firearm design
small arms
Most of the ammunition made by manufacturers in this industry is sold to private consumers: 44 percent in 1992, up from 40 percent of industry sales in the 1980s.
The major air rifle manufacturers are Gamo, Crosman, Benjamin, UTG, Daisy, RWS, Beeman, Mendoza, King Arms, Hornady, Beeman, Air Arms, Air Venturi, etcetera.
The classification of the bazooka as a small arm is a bit questionable. Although it was carried by an individual, it was served by a gunner and loader/ammo bearer, which made it a crew served weapon. Small arms are individual weapons.
Small Arms School Corps was created in 1853.
Royal Small Arms Factory was created in 1816.
Birmingham Small Arms Company was created in 1919.