Select min(date), max(date) and group by day from one column - SQL

Convert the column in the GROUP BY as well.

select
  min(datum), max(datum), CONVERT(varchar(8), datum, 112)
from
  dateTable
group by 
  CONVERT(varchar(8), datum, 112)

Here is a fiddle

Here are the list of convert values for dates. (I've chosen 112 for you in this case above)

In SQL Server 2008+, you can use the date data type instead of converting to a character string:

select cast(datum as date), min(datum), max(datum) 
from myTable
group by cast(datum as date);