Appealing authority in govt department

Dear Experts .

I have a query. I will be highly obliged if you can respond.

In one disciplinary case, the disciplinary authority  of state government  awarded one punishment (Dismissed). If they desired to modify/ alter/ reduce the punishment or withdraw the charge. are the department itself competent to do that? 

I mean can they reconsider their decision if we appeal to them?. Or only the tribunals/courts can consider appeal