I believe you are not reading the chart correctly. It is not showing what branch is 'above' another. The lines do not say this branch answers to that branch in any way. Just because the Sultansworn box is below the Syndicate box doesn't infer the one is "over" the other.
This is simply a chart that shows how each organization interacts with the others when martial force is necessary. In other words, it is saying the Flame General is not the General of the Sworn. He only directly commands the Immortal Flames, but can ask the Sworn for assistance.
The Sultana is not in the chart because she was not involved in the discussion that led to its creation.
{edit} Ul'dahn royal family, not families. It in no way infers anyone other than the house of Ul
This is simply a chart that shows how each organization interacts with the others when martial force is necessary. In other words, it is saying the Flame General is not the General of the Sworn. He only directly commands the Immortal Flames, but can ask the Sworn for assistance.
The Sultana is not in the chart because she was not involved in the discussion that led to its creation.
{edit} Ul'dahn royal family, not families. It in no way infers anyone other than the house of Ul