There are several type of Class 3 items that are restricted by the National Firearms Act.
Each state can impose additional restrictions on the sale, purchase, and transfer of class 3 firearms in addition to the compliance that is required with the national Firearms Act.
In Louisiana you can own the following items that are regulated the the National Firearms Act
Machine Guns (War relics only with written permission of Sheriff of Parrish)
Silencers Any Other Weapon (AOW)
Destructive Devices (DD)
Short Barreled Shotguns (SBS)
Short Barreled Rifles (SBR)
In Louisiana you cannot own the following NFA restricted items.
Follow this link to find out more about Louisiana and NFA restrictions on Class 3 Firearms