Is the command chain of the Imperial military in Star Wars ever detailed in canon?

Question

In the original trilogy films of Star Wars we see a number of "Imperial officers". Their rank, and indeed their branch of service is never made entirely clear. Nor is their relationship, in command terms with Darth Vader. They do, however, seem to have authority over the Stormtroopers serving aboard the various Imperial vessels.

In The Force Awakens the First Order troops are commanded by a Stormtrooper officer, Captain Phasma. While the First Order is obviously not the same as the empire, the Star Wars RPG did feature Kayn Somos, a Stormtrooper "commander", suggesting that the Stormtroopers did have officers within their ranks.

So I got to thinking about what would happens if one of these Stormtrooper officers were serving alongside an "Imperial officer" from the original films. Are they from different service branches? What are their respective ranks? Who would assume command?

All these sorts of questions would quickly be resolved if the service branch and rank structure of the Imperial military were ever detailed. Does any canon material at all attempt to address this?

Answer 1

TL;DR

There are 9 different services ("branches") of the Imperial Military.

The detailed part...

Battle Station Operations - Operate and maintain the Death Stars (+ other siege weapons in Legends)

Battle Station operations operated and maintained the first Death Star, and would have maintained and operated the second Death Star (if not for a number of rebels). Within Canon, there were a number of (mostly) self-explanatory subsections of this branch - Engineering, Logistics, Maintenance, Personnel, Security, Station defenses, Technical Support.

Imperial Academy - Train and enlist regulars and officers

This branch recruited and enlisted all personal for the Imperial Military. There were a number of institutions that specialized in each branch. Notable students include Biggs Darklighter and Mitth'raw'nuruodo (commonly known to us as Thrawn).

Imperial Army - Ground forces

Sub-units of this branch include:

• Administration
• Army Air Corps - Provide air support, e.g. TIE fighters and Airspeeders (TIE Strikers.) Nicknamed Groundhogs.
• Army Engineering Corps General Maintenance
• Imperial Armor Corps - They fielded AT-ATs, AT-STs (chicken walkers) and other Armoured Fighting Vehicles (AFVs) for the Army. A subsection called the Imperial Artillery Corps provided artillery, which can assume to include All-Terrain Defense-Turrets.
• Maritime Division - tasked with maintaining order and control on planetary waterways
• Military Police
• Special Forces command - special forces attached to the army, not clear why they are attached to army as opposed to Imperial Special Forces.
• Stormtrooper Corps - Provides all stormtroopers. The 501st Legion were a unit of the Stormtrooper Corps.

Due to a lack of content, it is not clear where the regular non-stormtrooper soldiers fit in, but it can only be assumed that they were replaced or part of the Stormtrooper Corps.

Imperial Intelligence - Espionage & Intelligence

Imperial Intelligence (also known as Military Intelligence, IM) were the espionage arm of the Imperial Military. Members of Imperial Intelligence included Death Troopers (as seen in Rogue One) and the Imperial Information Office.

Imperial Marines - Only detailed as a branch of the Imperial Miliary in Canon. Described in Star Wars Legends as Stormtroopers stationed on warships. They are also mentioned as being the units that will board other ships. It can be assumed therefore that these stormtroopers on the Tantive IV are Stormtroopers of the Imperial Marines:

Imperial Navy - Naval forces

Includes sub-branches for starfighters (Imperial Starfighter Corps), the Naval Military Police (separate from the Army Military Police) and Naval Command and Control (which can only be assumed to be the main command of Naval Forces.)

Imperial Special Forces - Special forces command

A term used to describe the special forces units of the Imperial Military. Units that fell under the Imperial Special Forces umbrella included Inferno Squad and the Storm Commandos. In Star Wars Legends, Imperial Special Forces often provided units for other branches of the Military, for example, providing Ghost Battalion to the Army and Imperial Navy Special Forces to the Navy.

Joint Chiefs - Command branch

A command branch of the Imperial Military, divided into Imperial High Command and the Naval chief. Imperial High Command also had a number of sub-sections:

• General Staff
• Imperial Security Bureau, a rival intelligence agency of Imperial Intelligence. Often wore white uniforms. Notable members include Wullf Yularen and Alexsandr Kallus (Agent Kallus from Star Wars Rebels.)
• Stormtrooper Command, commanded the Stormtrooper Corps (see Imperial Army)
• Battle Station Command, command agency for Battle Station Operations. Grand Moff Tarkin was the Head of this branch.
• Imperial Outer Rim High Command, in charge of command in the Outer Rim territories.
• The Admirality, commanded and administrated the Imperial Navy. A sub-unit of the Admirality, Fleet command, controlled the Navy's Capital ships, including Super Star-destroyers, such as the Executor.

Sector Command - Another command unit

Another command unit, not clear if part of The Joint Chiefs. Members include Commander Brom Titus and Captain Brunson. A sub-unit called Sector Command also existed.