The top-level in a WLAN is a Virtual AP. Here is an abbreviated version the output of "show profile-hierarchy:
ap-group
wlan virtual-ap
aaa profile
wlan ssid-profile
wlan virtual-ap2
aaa profile 2
wlan ssid-profile2
The question is, what do you want to copy?
If you simply want to make the wireless networks in one group, available on access points in another group, you simply clone the AP group, just like you did. What it does not change is the fact that other devices in the first AP group are still tied to the settings under the ap-group that you just cloned.
If you want to make changes to a setting so that it does not affect the previous AP Group, say the AAA profile, you need to (1) Make the change (2) save a copy (3) click apply.
The AAA profile is an exception in that you have to make the change to a AAA profile under Configuration> Security> Authentication. You cannot make changes to a AAA profile under Configuration> Wireless> AP Configuration> AP Group> Edit.