It happened at the Ilkeston Town FC match against Halesowen Town on January 29.
PC Adam Collins, of Derbyshire Constabulary’s football policing unit, said: “Fortunately no one was hurt but the pitch has been damaged, and it will be costly to replace.
“This type of behaviour isn’t acceptable, and we are committed to finding the person responsible.
“I would encourage anyone with information which could help our enquiries to get in touch.”
If you recognise any of the men in the picture or may have information which could help, contact police on the non-emergency details below, quoting reference 22*62668.
Facebook – send a private message to /DerbyshireConstabulary
Twitter – direct message the force’s contact centre on @DerPolContact
Website – complete the contact form at www.derbyshire.police.uk/ContactUs
Phone – call 101
You can also anonymously contact Crimestoppers on 0800 555 111.