Need help with script to export shared mailbox full access permissions and security group membership.

Pretty much every shared mailbox we have in our environment has a security group assigned to it that is the same name except starting with SG_.  I'm looking to have a script that can parse through all the shared mailboxes, review the security group assigned to it and export the members out with it.  I have something below but it's not complete and I'm unsure how to set it.  Any suggestions are appreciated.

Ideally it would output something like:

Mailbox Name     Security Group Name       Access

Mailbox1                 SG_Mailbox1                 domain\user1

mailbox1                sg_mailbox1                   domain\user2

MailboxABC            SG_MailboxABC              domain\userA

$sharedmailbox = Get-Mailbox -RecipientTypeDetails "shared" -ResultSize unlimited

foreach ($mb in $sharedmailbox) { 

$securitygroup = Get-Mailbox -id $mb | Get-MailboxPermission | where { ($_.User -like "domain\SG_*") } 
$securitygroup = ($securitygroup.identity -split "/")[-1]
#Write-Host "security group" $securitygroup.User

foreach ($member in $securitygroup.User) {

write-host $member
$SGMember = Get-DistributionGroupMember -Identity $member

Write-Host $SGMember

$outarray += New-Object PsObject -property @{
'Mailbox' = $mb
'security group' = $securitygroup.User
'SG Member' = $SGMember
}
}

}

$outarray