The Matukai were sometimes considered unusual in that for most of their existence, they have had no fixed organizational headquarters. Following the Twilight Schism, the Matukai have instead become nomadic warrior monks, wandering the galaxy in groups of as little as two to as many as five. Matukai traveling alone were also fairly common. During most periods of galactic history, the Matukai also seldom possessed more than fifty to sixty members overall in their order. An exception existed during three periods of time; in the days just prior to the rise of the old Galactic Empire, the Matukai had become several hundred members strong, their highest number in their order's history. By the time of the Yuuzhan Vong War, the Matukai had already begun to rebuild themselves and achieved great success, attaining some two hundred members before their numbers fell again from the extragalactic invaders. Following the war of the New Sith Imperium, the Matukai existed as just over one hundred members.
The Matukai had only four ranks within their order, with little to no specializations. Proselytes were the initiates, assigned to either the oversight of the Elders or a Savant mentor. The rank of Adept followed, as a Proselyte completed their training as a Matukai. Matukai experts were entitled to the rank of Savant, and often took the role of mentoring Proselytes ready for one-on-one training. Elders were the leaders of the Matukai, directing and guiding the Matukai under them. An unofficial, but still recognized rank among the Matukai is that of the Disciple, which were Force-sensitives, often of other Force orders, such as the Jedi Order, who undergo training with the Matukai. While they do not officially enter the Matukai hierarchy, they are considered honorary members nonetheless, and respected as such.
It was not a requirement for any Matukai to become instructors, although many did so regardless due to being part of their cultural identity to do so. Matukai instructors were not only permitted to take multiple apprentices, but it was encouraged in their tradition. Students were expected to learn from each other just as they were from their instructor, as well as support one another in their training. While outright rivalries were not supported, apprentices were also encouraged to jointly push one another to achieve the highest results from their training. As far as influence and authority are concerned, only the five Matukai Elders are entitled to commanding their brethren. All others, including the Proselytes, are considered to have just as much say in matters, provided they were of maturity; young children were obviously not included in significant decision making, for instance.
Culturally speaking, the Matukai generally spoke whatever language they chose, and were neither required nor expected to convert to one language over another, such as the Jedi Order, which encouraged the usage of Basic, if an individual's physiology held the capacity for speaking it. Consequently, Matukai could be found speaking dozens of languages as their primary tongue, such as Basic, Huttese, Mando'a, Bocce, Durese, Hapan and even High Galactic. However, all Matukai were taught to speak and understand the Matukai battle language, known as "Kendov'vun", which meant "the warrior's tongue". Used for a variety of purposes, all Matukai learned Kendov'vun as part of their training, although were not required to utilize it as their dominant language.