Woodpeckers are part of the bird family Picidae, which includes 
1/ woodpeckers,
2/ the piculets, 
3/ wrynecks,
4/ sapsuckers.

The Picidae are one of nine living families in the order Piciformes, 
the others being barbets (comprising three families), toucans, toucan-barbets, and honeyguides.

Piciformes, picidae, picus: woodpecker