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 New Mexico you can own the following items that are regulated the the National Firearms Act
Machine Guns Silencers Any Other Weapon (AOW)
Destructive Devices (DD)
Short Barreled Shotguns (SBS)
Short Barreled Rifles (SBR)
In New Mexico you cannot own the following NFA restricted items.
Follow this link to find out more about New Mexico and NFA restrictions on Class 3 Firearms