Remove site groups

I regularly create webs and subwebs with non-inherited permissions. This results in a bunch of permissions groups created for those webs. For some reason, deleting the web does not remove the corresponding groups. Since sometimes there are a lot, I decided to write a script to do this:

$web = Get-SPWeb <URL of root web>
$groupstodelete = $web.SiteGroups | Where-Object {$_.Name -eq "<whatever matching criteria>"}
$groupstodelete | ForEach-Object {$web.SiteGroups.Remove($_.Name)}

Simple and saves me a lot of clicking