A species that starts asexual juvenile. Grows to become a mature asexual with time. The time is probably similar as with humans. A mature asexual becomes female or capable of producing eggs when exposed to male pheromones. A female becomes male or capable of fertilizing eggs if not exposed to male pheromones and socially dominant. Sometimes when a breeding group loses its male this results in more than one male. They can share or split the group.
The ratio of females to males is based on assuming that eggs require more energy than fertilizing them. The eggs would be fairly large and laid into a special nesting pool guarded by the male(s). Fertilization is external.
Noukuulneimians have strong K-strategy, the juveniles are raised together by the entire breeding group. Once the asexual matures it can no interact with males without becoming female and is thus banned from the nesting pool area. It will still be able to interact with the females and in fact the breeding group is supported by the work of its asexuals.
When a breeding group is short of females it scouts nearby friendly groups for asexual deserving consideration and then "marries" the one they prefer. This results in groups being closely connected to larger societies. It also means there is a built-in degree of controlled breeding. Most asexuals die as asexuals working for their family and only the chosen ones pass their genes on. With males isolated to the nesting pools, the families would probably be controlled by the females.
I am not going into details, but you can assume the Noukuulneimians to engage in large scale building projects to create the shallow water environments they prefer and have social organization and planning ability sufficient for large scale projects.
Finally, the actual question
How would this reproduction system affect society?
Would the wider society be guided by females networking with their siblings at other families? Or by asexuals working at larger scale organizations? Would there be value to private property in addition to family property when you presumably work for your family in hopes of "retiring" to another family? Is the answer different for asexuals and females? Say asexuals gather wealth to prove their value to possible families and then give it all to their new family. Any other effects I need to consider when I start thinking about the society?
If I get reasonable answers, I will do follow ups with physiology and ecology, so no need to speculate about them here.