There are two types of groups in OpenAccess, the logical group and the physical figGroup. They use different commands, you have them mixed.
group - Logical connection between objects. Usually used by applications, no interactive editing support. Abutment used a group for tracking.
dbCreateGroup, dbAddObjectToGroup, dbRemoveObjectFromGroup, dbGetGroupByName.
figGroup - Physically joins multiple figures, edit as a single object. To programmatically edit all the objects in the figGroup, edit the figGroup object.
dbCreateFigGroup, dbAddFigToFigGroup, dbRemoveFigFromFigGroup, dbGetFigGroupByName