One interesting thing not mentioned thus far is the Cuahchiqueh were typically thought of as fighting in pairs. When picturing this, keep in mind that the Cuahchiqueh, Otontin, Cuacuauhtin, and Ocelomeh were not an officer corps leading the general troops, but were military orders of elite professional soldiers. They would be fighting among the general army (which had its own rank system), but think of them more like special forces than forming a military command structure.

The other thing to keep in mind is that, by the time of Spanish contact, these military fraternities were the province of the nobility. While the Mexica pre-Imperial and early Aztec Imperial periods saw a more meritocratic system, the social system significantly hardened starting with Motecuhzoma Ilhuicamina, who became tlatoani in 1440. One interpretation of the exclusion of commoners from the military orders is that being part of the nobility was always a requirement, but that the practice of appointing Cuauhpipiltin (Eagle Nobles) made this essentially meritocratic. These were non-noble individuals who could earn a (non-hereditary) noble status via military success by taking captives and performing brave deeds. This practice, however, was ended at some point during the Aztec Imperial period.

I'm making this seeming digression to note that since the military orders were the province of the nobility, this solidified the elites as a professional military class. To be noble was to wage war and to wage war was to be noble. The practice of one could not be excluded from the other. The fact that success on the battlefield would also result in the awarding of valuable gifts (or even private lands) from the ruler further led to a melding of nobility, militarism, and economics.

This comes into play when interpreting the xochiyaoyotl (flower wars), which are often seen purely in religious/ritual terms, but actually had more realpolitick underpinnings. While not always waged outside of the normal winter/dry military campaign season, they could and were undertaken at times when the mass of the populace would be engaged in agricultural activities. They required a professional military class, in other words, while at the same time allowing for the continuation of warfare outside the window the mass mobilization could be accomplished.

In addition to all this, the xochiyaoyotl served as a way for this professional military elite to earn status and experience through these smaller scale conflicts. The military orders required nobility to enter, but also required personal success in battle. The flower wars provided greater opportunity for this, which in turn meant it afforded greater opportunity for wealth and status.

Anyways, the point is that this was a hugely interconnected rational system.

As for why there is a dearth of information on the military orders, this is more a result of our sources for pre-Hispanic Mesoamerica coming from post-Hispanic Mesoamerica. Some of the most important sources we have for these institutions come from information gathered in the very early colonial period, when people who had lived with Cuachiqueh as a social reality were still alive. Many of these works, such as writings by Spanish friars like Sahagún and Durán, were either suppressed at the time or conveniently lost for a few centuries. Writing about the military glories (or religious practices) of the pagan Aztecs was not exactly a booming business in the Christian colonial period. As result, we have limited primary sources, and the slow process of generating English translations of Spanish and/or Nahuatl texts means this information has been even slower to reach the Anglosphere.

Follow-up question: Was their rank of any specific religious significance?

I would like to learn about The Aztec. Any links?

Well, physically, they were known as the "Shorn Ones" due to the fact that they shaved their heads with the exception of a lengthy braid on the left side (some accounts say that it ran through the middle as well). They were also known for painting their heads yellow on one side, and blue on the other.

Interestingly, the Cuachiqueh made an oath to not step backwards during a battle, or they would likely face death by their fellow warriors. The tlacateccatl, a rank which is roughly equivalent to that of a general in the Aztec military, was usually a member of the Cuachiqueh.

Other accounts state that one could only become a member of the Cuachicqueh if they captured six warriors. All in all, they were a very elite warrior force.

The majority of this information was found on www.ancientmilitary.com and this article.

Any good resources on the jaguar and eagle warriors?