The major "groups" that you are referring to are probably the different orders of birds, so here goes:Struthioniformes

Tinamiformes

Craciformes

Galliformes

Anseriformes

Turniciformes

Piciformes

Galbuliformes

Bucerotiformes

Upupiformes

Trogoniformes

Coraciiformes

Coliiformes

Cuculiformes

Psittaciformes

Apodiformes

Trochiliformes

Musophagiformes

Strigiformes

Columbiformes

Gruiformes

Ciconiiformes

Passeriformes

The sacrament of Holy Orders can only be administered by a Bishop, which includes, of course, cardinals and the pope as they are bishops.

Traditionally, Orders were split into minor orders and major orders, though the minor orders and the subdiaconate have since been suppressed following Vatican II. Properly speaking, the ordination to priesthood is what constitutes the sacrament of Holy Orders since all the other orders are automatically received, if not already possessed, by virtue of the sacrament.

Minor Orders:

Porter

Lector

Exorcist

Acolyte

Major Orders:

Subdiaconate

Diaconate

Priesthood