Art is right...the shroud around the base should be removeable. Meanwhile, some clues:
If it has a 1" discharge it's most likely a Jabsco...37010 if it uses sea water, 37045 it uses pressurized fresh water. However, it appears to have a 1.5" discharge, which would most likely make it a Raritan SeaEra.
If it's a sea water version, the SeaEra has a diaphragm intake pump at the end of the pump/motor assembly that's easy to access to replace the diaphragm...the Jabsco 37010 has an intake impeller that's impossible to access without taking the whole d'd thing apart.
There are a few other clues in the exploded drawings of both that should help you ID if you can't find it after you remove the shroud.
Raritan SeaEra Parts List and Drawing
for the sea water version...part #162000W is the intake pump assembly The fresh water version won't have an intake pump. Note that there are TWO repair kits--intake pump assembly and discharge pump assembly.
Jabsco 37010 owners manual
Drawing and parts list are on p 3 & 4.
It also appears that the discharge hose has been spliced (somebody didn't measure corrrectly?) You need to add another clamp 'cuz all sanitation hose connections should have TWO clamps, with screws 180 degrees apart.
Peter, no way use the bowl to narrow down a toilet mfr because all mfrs including Jabsco, Raritan, Tecma and TMC use bowls that mount using a 4 bolt + pattern.