Ok.....where are you flying from and to? If you called CO and asked about CO6566, the information on CO's website shows that this a code-share flight operated by UA from Sacramento to Philadelphia with a stop in Denver. UA's website shows that UA6566 is operated by United Express and goes from Salt Lake City to San Francisco.
If you asked about CO6904, CO's website shows that flight is operated by United and goes from Denver to New Orleans. UA does not have a flight 6904.
It is confusing but you need to look at the airline designator in front of the flight number and plug that into that particular airline's website. It will then be VERY clear as to which airline operates that flight. Click the link below and you will in very big letter and numbers in parenthesis which airline operates the flight.
CO's website showing CO6904 is operated by United