I honestly don’t know a single advantage of using the Group function in SketchUp. When working with my model I always make components and not groups. Components share a relationship between copies while groups do not. Even when joining multiple components I always use the component command and not a group command.
Let’s say you make a 2×6 that is 96″ long. After you make it a component you need to duplicate this 2×6 four times to make a table top. After you do this you realize that the table is just too long. Because you copied a component any modifications you make to either the original component or the copies will be updated among all of them. Double click to edit one of your 2×6’s and change the length using the push pull tool. You will notice that all of the copies will update. If you do not want one of the copies to update or you want to take one of the copied components and make it into a new stand-alone component you can right click and select Make Unique. This means the copied component is no longer a copy and now a unique component. Anything you do to this unique component will not be updated among it’s previous copies.
Modifying copies of groups will do nothing to the other copies. Groups do not share a connection among one another. I ALWAYS use components and NEVER use groups.