The Galactic Empire: An Empire Reborn
Imperial Officers' Manual
Major Revision: 2.0 – 2008.10.31
An adaptation of the pre–Endor document and policies.
RIP  cylinders
... A Commodore's Rank Insignia ...

Within the standard Imperial Navy, the rank of Commodore (CD) is held by Systems Force Flag Officers.

Although -- in technicality -- the rank of Commodore does not constitute "full & true" admiralty, it is classified as a lower variant of admiral for all intents & purposes... It is at this rank that the authority of a naval officer truly begins to extend to multiple units, or larger sections of the Empire.