Development :
Founded in FY1021 during the War of the Hundred Years by Lothair Mantelar.
By approximately FY1111 the Children of the Light had become a full fledged military society, with very strict ascetic beliefs, they are dedicated to the defeat of the Dark One.
They are sworn to do battle only against Darkfriends and Shadowspawn.

This is good news, if the Children's oath is just the above, and doesn't also include a personal vow of loyalty to the Lord Captain Commander or anything like that. We know that Whitecloaks swear for life, and if the above is all that Galad is sworn to then he can do what he wishes, when he wishes. However it does mean that he wouldn't be easily able to fight the Seanchan for example.

However the definition of Darkfriend is left to the individual.
By law any channelers are to be arrested or exiled, but in actuality most are killed while "resisting arrest".

Organisation :
Each society is controlled by a high-ranking individual.
In the Dome of Truth the commanders of the Children gather to determine policy for the entire organisation.
Lord Captain Commander presides over the Council of the Anointed, which consists of approximately a dozen of the highest-ranking, and most favoured Captains, as well as the High Inquisitor.

The 'most favoured' indicates that the Council can be loaded with the Lord Captain Commander's friends, so he's probably not as constrained as the Amyrlin Seat, which makes sense when you consider that the Children are essentially a military organisation.

The High Inquisitor - currently Rhadam Asunawa - ranks only slightly below the Lord Captain Commander. Though command for the military originates with the council, he alone issues the orders for the investigative Hand of the Light.
Members of the Hand serve as interrogators or occupation forces.
Note: Lord Inquisitors are equal in rank to Lord Captains.
Many of the Lord Captains also have their own personal networks of eyes & ears.

Insignia :
Officers' cloaks and tabards are further adorned with silver lightening bolts for under-officers, and golden stars or knots in increasing number to indicate rank for higher officers.

Military Organisation :
The Children of the Light are always deployed as mounted cavalry, usually in groups of about one hundred.

I'm not convinced that that makes sense from a military POV. The overemphasis on cavalry is understandable on the part of say the Tairen Nobility, but are we really to believe that one of the Great Captains, Pedron Niall, would allow his force to consist entirely of cavalry ?

A Lord Captain usually commands a Legion, which is officially two thousand men, but may actually be larger, and is often smaller.
Below the Lord Captain the ranks are Senior Lieutenant, Lieutenant, and Under-lieutenant.
Under those is the Hundredman, one who theoretically commands a hundred soldiers. In practice, the actual number varies widely.
The number of Legions within the Children varies at any given time. Not all units are organised into Legions, and not all are commanded by a Lord Captain.
When a Lord Captain commands a unit or Legion the Lieutenant chosen as second-in -command is given the temporary rank of Second Captain to differentiate him from any other Lieutenants within the unit.
Below the officer and Hundredman are Bannermen, with Second Bannermen below them, then Squadmen and Second Squadmen.
Below these are the file leaders and the regular soldiers.
Soldiery have been loaned to the Questioners, but the reverse does not happen.