Given an altcoin, how to find its mining pools? I wonder if it can be possibile to find all pools for a given altcoin. 

For example, if an altcoin X has an official pool P and its official pool crashes or its not working, how we can find all the pools for the given coin? 

It is supposed that the other pools aren't indexed on search engines.
It is impossible to identify who a miner or mining pool is based upon the coin's blockchain. If the mining pools are private or have poor search engine optimization, then it will not show up in search engine results. Given that you cannot deanonymize miners from the block data nor can you search for all of them, you cannot get a definitive list of mining pools for any coin.