This article talks about on how to add a security group in O365
Security group in O365
In O365, Security groups give people access to resources such as SharePoint sites. They can also include devices, for use with mobile device management.
steps to add a security group in O365
Open O365 admin center: https://admin.microsoft.com/
Navigate to Teams & groups –> Active teams & groups –> security groups –> add a security group

fill in all details ( see below )

Review and finish it

Done

You can manage it from here

PowerShell script for above manual task
# Install Microsoft Graph module if not already installed
# Install-Module Microsoft.Graph -Scope CurrentUser
# Import the module
Import-Module Microsoft.Graph
# Connect to Microsoft Graph with the required permissions
Connect-MgGraph -Scopes "Group.ReadWrite.All"
# Create a new security group
$group = New-MgGroup -DisplayName "MySecurityGroup" `
-MailEnabled:$false `
-MailNickname "MySecurityGroup" `
-SecurityEnabled:$true `
-Description "This is a security group created via PowerShell"
# Output the group details
Write-Output "Security Group Created Successfully!"
Write-Output "Group ID: $($group.Id)"
Write-Output "Group Name: $($group.DisplayName)"
security group vs mail-enabled security group
A security group is primarily for controlling access to network resources, while a mail-enabled security group adds the capability to send and receive emails to all members of the group, functioning as a hybrid of a security group and a distribution list. Mail-enabled security groups can also be added to Microsoft 365 Teams, but cannot be dynamically managed through Microsoft Entra ID and cannot contain devices as members.
Conclusion:
Post reading above article, reader will be able to add a security group in O365 successfully.
You can also read this article https://microbrother.com/how-to-add-a-distribution-list-in-o365/ to add a distribution list in O365.
Thank you ☺️