There are really only three venting options.
Venting bathroom exhaust fan through wall.
If you vent through the roof condensation will drip back into the interior.
The exhaust duct using solid metal steel in this case is routed through the ceiling out over the wall top down through a soffit or roof eaves overhang and then enclosed against pest entry.
Ductwork is what will connect the fan to the outside.
Wiring for the exhaust vent fan light is routed to wall switches that in this case will turn on the fan if the light over the shower is also switched on.
Wall mounted vent fans are available though they re not as common as ceiling mounted models and may be more difficult to install especially if you have a brick veneer house.
If you vent through a soffit where attic vents are often located the moisture will get sucked back up into the attic or roof venting.
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.
There aren t many options for routing an exhaust fan to the outside of the house.
There are ductless vent fans that use a charcoal filter to remove odors but they do not remove excess moisture which is the main purpose of a bathroom vent fan.
Amazon s choice for through wall bathroom exhaust fan broan nutone 512m through the wall ventilation fan white square exhaust fan 6 0 sones 70 cfm 6 4 5 out of 5 stars 765.