When you want to schedule a dashboard refresh, you create a new public group or you want to use an existing public group and want to email your dashboard refresh to this public group. But, you are not able to search and select this public group. Why???

This is because the public group that you want to email the dashboard refresh should also have access to the dashboard folder.

Navigate to the dashboard folder -> Edit -> Grant Access to section and Add the public group. The group will now be available for selection while emailing dashboard refreshes.

If you have granted access to "All users", then this problem will not occur.