Typically an exhaust fan that is vented through the roof has a roof hood or roof cap which allows air to exhaust but provides protection from wind blown rain.
Vent bathroom fan through roof or wall.
These are usually installed on a pitched roof.
If you want to vent a bathroom fan through an exterior wall you will have to cut a 3 inch or 4 inch hole with a hole saw drill bit.
Choice is go up to roof 5 6 feet or out the present vent 15 18 feet with insulated pipe or shorten the line by going straight to side of home but this requires going up high with latter to drill a new vent hole as tight quarters in attic prevent drilling from attic.
From up on the roof use a jigsaw or reciprocating saw to cut a 4 in.
Leave the drill bit sticking through the roof so you can find the hole.
It is because of this that many builders tend to advise against this method.
Try to keep it close to the fan location.
Going to the soffet is 12 feet.
This involves running ductwork from the fan usually though an attic and out through the roof.
Broan sells an inexpensive model which is probably available at any big box store.
Depending on the location of the bathroom it may be easy to vent the exhaust fan through the roof.
Will be usually fed.
Start in the attic and drill a hole through the roof in the desired vent location.
If your exterior siding is vinyl or fiber cement you will have an easier time cutting the hole.