If your organization pays for Google Apps, and if you have a Windows PC, you can setup Outlook to sync with your Google Apps account using the Google Apps Sync tool. And since TntConnect has good support for syncing contacts with Outlook, this is a great way to go!
The Google Apps Sync tool creates a new Outlook profile, so you'll have to specify this new profile in TntConnect. Under the "Tools" menu, click on "Microsoft Outlook", then "Settings for Sync with Outlook":
Here you can also specify any special sub-folders for Contacts (or Calendar) that you'd like to synchronize with.