If it's an exterior wall, it could be an early cavity (depends where you live) but more likely it's solid brick or stone. If it was a fairly posh house the walls could be "studded off" ...... ie 2-inch (50mm) battens finished with lath and plaster, so you'd need to drill a few exploratory holes to find the studs. (As long as you don't have expensive wallpaper.)
If it's an internal wall, then most likely studwork with lath & plaster. Again, you need to search for the uprights. (If you drill a few 3mm holes in the area that will be covered by the mirror, they won't be seen. Find one stud....... then the others will be 16 inch (Imperial) centres.
If you're really stuck, then cut a piece of 9mm plywood to a size smaller than the mirror.......... and fix to the wall ......... then screw the mirror fixings to that.
Fix the ply with rawlplugs into the plaster ....... and "Grab Adhesive" to glue the ply in place. It'll carry the weight OK, but will rip off some plaster if you ever decide to move it :o(