The term "greatest" is so ambiguous in this context that this is hard to answer. To provide some context the fleet involved in the invasion of Normandy was massive in sheer number of ships. Each of the five invasion beaches had supporting fleets upwards of 5000 ships. But the nature of the English Channel meant that smaller ships with short range could be involved in the invasion, and most of the ships were troop transport, support and supply.

As far as combat ships, the Normandy invasion fleets were dwarfed by fleets involved in the Pacific. The Normandy invasion fleet included 6 battleships, 23 cruisers, 101 destroyers and a number of smaller ships. In comparison, the initial invasion of Okinawa involved approximately the same number of troops with a supporting fleet of 18 battleships, 27 cruisers, 177 destroyers/destroyer escorts, 11 fleet carriers, 6 light carriers, and 22 escort carriers. In total there were only about 1500 ships though as they had to be able to make the journey from Hawaii or closer bases in Guam or the Philippines.

Had the invasion of Japan occurred it would have likely dwarfed the invasion fleet at Normandy. D-day involved approximately 160,000 troops. The first phase of Operation Downfall, which was the invasion of Kyushu, labeled Operation Olympic was slated to have over 600,000 troops. The follow-up invasion of Honshu, Operation Coronet, was to include over 1 million troops. I am not aware of a complete list of ships including support ships planned for the invasion, but the warships planned to be in the combined Third and Fifth Fleets for the invasion included 19 battleships, 20 fleet carriers, 7 light carriers, 61 cruisers, 63 escort carriers, and 315 destroyers. Had Japan not surrendered and Operation Downfall occurred, it would have probably been the greatest armada assembled in human history.