Question: 

I am trying to edit a pre-existing group created in SalesLogix client. When I view the SQL query, I see that there are conditions applied to this group. However, I do not see the 'Conditions' tab in Query Builder. How was the previous user able to set the conditions?
Also, can groups be not edited through SLX Architect?

Answer:

Groups cannot be edited through the SLX Architect, but you could change Ownership and Manage Releases.

If you don't see a Conditions tab, you are Dealing with an Adhoc Group, and that means that you can't change the conditions, the members were added one by one with no Queried criteria. As this is done, the ID is preserved on the ADHOCGROUP table.

The Condition that you see on the SQL view is more than likely the filtering being applied against the ADHOCGROUP table to retreive records that have been added to the Group.