Gimme the codes! powers, activate!
$Groups = Get-ADGroup -Properties * -Filter * -SearchBase "OU=Groups,DC=corp,DC=ourcompany,DC=Com"
Foreach($G In $Groups)
The point being, just take your time and break it out into steps. I know that it's fun to try to get everything and the kitchen sink to fit into a one-liner with Powershell, but it's by no means required.
A few notes:
You don't need to do
Get-ADGroupMember if you collect the Members property in the initial
Get-ADGroup Cmdlet. The good thing about this is that it halves the amount of calls you have to make to AD, which should make your script run faster, and it eases the burden on the domain controller.
$G.Members will display all members of the group $G... in Powershell 3. In Powershell 2, you might still need to put another Foreach inside the Foreach there to enumerate through the group members. (Yo dawg, I heard you like loops...)
Write-Host here, which is gross. You should never really use
Write-Host. Instead, you should be building and outputting objects, not text, but that was a whole other topic and I was too lazy to do that for this answer.