How many star destroyers were in the Imperial fleet during its zenith?

There were 25,000 Imperial-class Star Destroyers in the Empire at its zenith.
There are numerous quotes to that effect, most specifically a Technical Manual quote specifically saying 25,000 Imperial Star Destroyers.

That a galaxy-spanning Empire would deploy ad hoc detachments of capital ships to divergent areas based on strategic, economic, or political significance, and that the highly modular Sector Group Order of Battle would not be properly followed in dozens if not hundreds of instances is to be expected. In fact an IU exchange between Imperial Army and Navy officials on that exact point was in the Imperial Sourcebook.

As presented in the Imperial Order of Battle the Imperial Star Destroyer is the backbone of the Sector Group; the OoB calls for a minimum deployment of 24 ISDs per SecGrp, and as many as 80 in a fully augmented SecGrp.

Arguments that the 25,000 number should include non-Imperial designs always crop up, which is ironic because even the early WEG ISB specifically consigned Victory-class Star Destroyers to auxiliary roles in specialized Heavy Squadrons and specifically tagged Imperial-class vessels as the categorical necessity in all Battle Squadrons.

In the same instance, despite a single line on the Cracken's Threat Dossier that Super Star Destroyers should serve as a Sector-level command ship, there is no actual place in the known OoB for Star Dreadnoughts (or lesser Supers).

At best we can average the number of ISDs per SectGrp to 24, though we know numerous groups have barely any and others, such as the forces collected under Oversector Outer, during both Tarkin and Kaine's Moffdom, exceeded that number.

Also, the stated reality that 50% of Star Destroyers are deployed in the core should not be surprising, as it is likely the core represents a majority of the planets in the actual Empire.

Recall just how sparse space in the Outer Rim actually is.

 

You know, I never thought about that. I would love to know the exact number.

 

Likely because ships heavier than a Star Destroyer are not usually assigned at the Sector level in any sort of numbers, but are part of Regional and Strategic units. The ones assigned to Sector groups are usually single ships, and thus designated as command units, probably due to larger vessels having more C4I facilities aboard. Using the definition of Super Star Destroyer as any ship larger than an ISD or Tector, the CTD quote fits, with Sector Fleets being assigned a single larger ship as a command unit.

 

The quote from CTD:
"Each Imperial-class Star Destroyer is a mobile command base. The Super-class Star Destroyer was designed to be a sector-level command base and the Death Stars were to be the center of regional commands."
They're talking specifically about the Executors and what they were supposed to be - of course, note that the Death Stars obviously didn't end up filling their projected roles, and considering that there were only four active Exes by the Battle of Hoth, it's doubtful they were fulfilling their designated role either.
Presumably we'll see more about it, though, when the EGTW comes out.

 

On a similar note, prior to and during the CW, we see Lucrehulk-class vessels used in the center of formations that involved either blockades or ground invasions, either as command ships or heavy support vessels. During the Wars, we have larger vessels like the Subjugator-class and the Maelstrom going on long-distance strike missions.

Similar vessels would obviously be capable of being produced by the Empire, given its larger industrial base and available resources. Even with the Executor-class being intended for the sector command role, the vast majority of Executors are only seen posted to important systems in the Core or to a select few commanders, hardly a common sector command ship. The smaller SSDs mentioned in ITWT would be more befitting to the roles we see the CIS Lucrehulk and Subjugator classes perform decades before. As of now, we mostly have stationary examples of C&C vessels in the Empire, the Cardan-class battle stations, the Derilyn space defense station etc. Interestingly enough, the Battle of Mon Calamari in DE shows something more similar to the CW situation, a Lucrehulk-sized command ship, the Allegiance, leading a blockade of Star Destroyers over the planet, while several heavier vessels attack the world below. A more augmented version of invasions we see in the later seasons of TCW (with multi-km destroyers, smaller frigates, large battleships and a command ship, usually a destroyer, battleship or frigate).