The soap dish tile remove the grout around the tile with a grout saw.
Replace soap dish tile wall.
Use thin set and hold your new soap dish in place using long strips of duct tape crossing the new dish tile.
Regrout after 24 hours.
Remove the broken soap dish a fractured soap dish may almost fall off the wall by itself.
Shower soap dish holders do not last long.
Install a replacement soap dish of either the retrofit style or in plain tile.
Install a 1 4 inch masonry bit.
Place masking tape over the tile.
Loosen the old grout if the soap dish has fallen entirely off the wall you can skip ahead to the third step.
The tape will help keep the drill bit from slipping and ruining an adjacent tile when.
To help it shatter drill.
Clean the area the new tile will not.