Draggable Groups (Specific 'Dragging Point')

I want to make it so the user drags the blue part of the group, and it moves the entire group around.
I know its possible to make draggable groups, but it seems the only way to do it, is to make it so the entire group can be dragged from any location on the group. (Instead of just a single location)

(Also the information displayed is mearly fictional)

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