What have you tried? What "doesn't work"?
Is this what you are looking for?
exp = (a \[Implies] b) \[Or] c
AssociationMap[BooleanConvert[exp, #] &, {"DNF", "CNF", "NAND", "NOR"}]
(*
<|"DNF" -> ! a || b || c, "CNF" -> ! a || b || c,
"NAND" -> a \[Nand] ! b \[Nand] ! c, "NOR" -> ! (! a \[Nor] b \[Nor] c)|>
*)
