Hi,
I think that the "group" table was present in an older version of Joomla, and is no more present now.
Firstly you could potentially create a new table named "xxxx_group" with the columns "name" and "id" and see if the group asignation is working, and if you still have the query error.
Else you will potentially have to check in the akeeba component the code calling that part for the subscription, probably in a class named "subscription" and in a "save" function.
Aren't there any topic in their forum talking about that ? It is no more supported, but the question had potentially been asked before the end of the support.
There is not yet developments in that direction, but it is still on our todo list. Once we have finished other main tasks on our todo list we will look deeper at this functionality.