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316th Funklenk Panzer Company had 6 Tigers and 9 Stugs, but in June 1944 only 3 of the Tigers were operational. It is difficult to establish whether or not these Tigers were Tiger I's or Königstigers as both types were issued to these specialist units with their remote controlled demolition vehicles.
DPT
[EDIT]
Günter's excellent website suggested above states there were indeed 3 Königstigers with this unit. If we add these to the Königstigers operating in the 1st Company of Abteilung 503 then we still only get a potential 15 Königstigers in Normandy at any given time. (Unless someone knows of some other Königstiger equipped units?)