When you create different profiles using Connector and display the icon on the application, I have noticed that it displays an icon for searching and another which groups scanning and importing together. If you were to create a profile for each type of action available, how many different icon groups would you see in an application?
Connector Profile Icon Groupings?
Any profile can be split out into it's own icon or grouped together, even ones of the same type. Try right-clicking on the profile buttons and see if the option to split is there (If not, the profiles might be setup to not allow users to move them around, which can be tweaked in the profile xml).