Move apps left and right on the taskbar

I always tend to group the tabs that I'm working on within Firefox by simple drag-and-dropping them left and right. I would like to do the same thing with the programs I have active in my gnome taskbar at the low end of the screen.

I am not knowledgeable at all of what's going on under the hood. I just use it for my every day applications. But if this would be possible it would be great and would spread the word of Ubuntu even more than I am doing now!!