The basic organizational unit is known as a Teocalli. "Teocalli" is defined as a God-house or temple that surmounted a terraced pyramid commonly found in Mesoamerica, which is where the legend of this order stems from. Local Teocallis falls under the governance of the Supreme Teocalli, but the Teocallis are given a lot of autonomy. There are Teocalli in United States, Canada, Mexico, and Panama. Members of this order are known as "Artisans." There are two degrees conferred by this order: Artisan and Master Artisan.
A Teocalli is led by the following officers:
Camaxtli (presiding officer)
Chimalma (similar to a VP)
Huemac (similar to a VP)
Titlauacan (similar to a VP)
Cuatemoc (Inner Guard and Guide)
Netzahualcoyotl (Outer Guard)
High Priest or Teopixqui (Chaplain)
Teocallis can come together and form regional associations which are presided over by a Chief.
If Nobles are interested in forming a new Teocalli, they need at least 15 Shriners that reside in the same jurisdiction as their Shriners Temple, are in good standing, and a Teocallis doesn't already exist in that jurisdiction. Then they would contact the Supreme Teocalli and petition for dispensation.
The Order of Quetzalcoatl was founded on March 14, 1945, by Arthur J. Elian in Mexico City. He was a scholar of ancient Mesoamerican history and of Mexican lore. He was also a very involved Mason having been elected as Grand Master of the Muy Respectable Gran Logia Valle de Mexico as well as being recognized as Emeritus Registrar and 33° of the Scottish Rite of Mexico, and Recorder Emeritus of Anezah Temple. Not much is known of the formative years of the order, but the order spread after Shriners from Arizona and California had made trips to Mexico City and were initiated into it. They carried it back to the US where it spread over the years and eventually led to the formation of the Supreme Teocalli.
This order takes its name from an ancient Mesoamerican god by the same name. Quetzalcoatl is known as the Plumed Serpent and his name comes from the Nahuatl words "quetzalli" meaning "precious feather" and "coatl" meaning "serpent". Quetzalcoatl was a storm god who was considered the creator of the world and mankind, and is often associated with the rain god, Tláloc. He was considered patron and god of learning, science, agriculture, crafts, and the arts. In Aztec mythology, he was the brother of Tezcatlipoca (god of night and sorcery), Huitzilopochtli (god of war, the sun, and human sacrifice), and Xipe Totec (god of spring and vegetation). Other legends state that he was a prophet and leader of a group of men known as the Toltecs (craftsman or builders) who was then deified after he had attained such enlightenment that merited his ascension.
Once a Noble accepts an invitation into the order, he is obligated as a Coate or tribesman. Within one year of that happening, he must receive the Artisan degree. Within two years of becoming an Artisan, one must obtain the Master Artisan degree during the Feast of Fire (their annual business meeting). It also seems like one can attain Master Artisan by going on a pilgrimage to the Temple of Quetzalcoatl at Teotihuacan (north of Mexico City) or Chichen Itza (Cancun).
Brief History of the Name Quetzalcoatl and the Toltec Ancestry of the Order. (n.d.). Retrieved from Supreme Q: https://www.supremeq.com/menu_bar/history.pdf
Cartwright, M. (n.d.). Quetzalcoatl. Retrieved from Mukilteo Teocalli Number 111: http://teocalli111.org/page6.htm
Order of Quetzalcoatl. (n.d.). Retrieved from Wikipedia: https://en.wikipedia.org/wiki/Order_of_Quetzalcoatl