Do you get any error message when you try?
The DNS system itself has a limitation. You cannot use a CNAME record if you have any other records in your zone with the same subject (the same value on the left side).
So using your own example, you can't have any other records with network on the left side. If you must, then you cannot do what you want in DNS but may be able to do it with an A record to a permanent redirect.
Jeff