When to use an assertion and when to use an exception

Most of the time I will use an exception to check for a condition in my code, I wonder when it is an appropriate time to use an assertion?

For instance,

Group group=null;
try{
    group = service().getGroup("abc");
}catch(Exception e){
    //I dont log error because I know whenever error occur mean group not found
}

if(group !=null)
{
    //do something
}

Could you indicate how an assertion fits in here? Should I use an assertion?

It seems like I never use assertions in production code and only see assertions in unit tests. I do know that in most cases, I can just use exception to do the checking like above, but I want to know appropriate way to do it "professionally".

Assertions should be used to check something that should never happen, while an exception should be used to check something that might happen.

For example, a function might divide by 0, so an exception should be used, but an assertion could be used to check that the harddrive suddenly disappears.

An assertion would stop the program from running, but an exception would let the program continue running.

Note that if(group != null) is not an assertion, that is just a conditional.