Goldfish (Carassius auratus) are in the order of "Cypriniformes".

Piranha

Order: Cypriniformes

Family: Characidae

Genus and Species: Serrasalmus nattereri

Here's the entire Classification.

Kingdom: Animalia
Phylum: Chordata
Class: Actinopterygii
Order: Cypriniformes
Family: Cyprinidae
Genus: Carassius
Species: Carassius auratus

Minnows constitute the family Cyprinidae of the order Cypriniformes. Most of the members of the minnow family are only a few centimeters in length, but India's mahseer measures up to 2.7 meters and some weigh more than 45 kg. Minnows are the largest family of fish, including more than 2,000 species. They are characterized by a single dorsal fin and by one to three rows of teeth in the throat but never in the jaw.

The goldfish comes under the class "Actinopterygii" order "Cypriniformes" family "Cypriniae" genus "Carassius". Its binominal (Taxonomic) name is "Carassius auratus" (auratus meaning golden or of gold)