I was talking to my elder daughter the other day about this question: what is the world's oldest extant organisation?
The obvious candidate would be the Catholic Church, since it's approaching its 2000th birthday.
I think we can do better though. My suggestion for the oldest organisation in the world is the Egyptian Public Service.
Egypt is recognizably the same country it was when Menes united the upper and lower Egypts in about 3100BC. He must have created an organisation to run the place and I'm sure every Pharoah inherited it from his predecessor.
Even in periods when Egypt was thoroughly invaded by Persians, by Romans, by Muslims and by the French, there probably remained a small core of public servants, somewhere, who kept the basic wheels of government running. (I'm talking about the public service here, not the governments that commanded it.)
I don't think there was any period when Egypt was so destroyed that there was no administration of any sort. (Someone who knows Egyptian history better than me might correct that.)
If so, then the world's oldest organisation is a bit over 5,000 years old.