* 4-speed automatic: This was a common transmission in many HHR models.
* 5-speed manual: A manual transmission was also available in some years and trims.
There weren't any other widespread transmission types offered from the factory. While it *might* be theoretically possible to swap in a different transmission from another vehicle with significant modification (a very complex and expensive undertaking), it's not a practical or recommended approach for most people. Sticking with the original transmissions (or a replacement of the same type) is the easiest and most reliable option for repairs or replacement.