How old is your dog?
Is your dog a male or a female?
Is your dog healthy?
Is your dog overweight or the proper weight?
Does she have arthritis or sore joints?
Does she circle around before getting comfortable?
How much exercise does your dog get daily? What type of exercise?
Thanks for your reply. From your answer, the sighing or groaning does not seem to be due to any discomfort or health problem (since your dog seems to be young and healthy without any joint problems). However, if in doubt, it would be worthwhile to bring this up to your veterinarian on your dog's next scheduled visit.
My guess is that your dog is just sighing or groaning in relaxation/comfort after getting her spot exactly how she wants it (i.e. by circling) - my dog actually will dig at and rearrange her blankets to her liking and I have heard her moan in content as she settled down.
I'm not sure what breed your dog is, but some breeds do much more "talking" i.e. vocal expression than others (also some individuals do much more "talking" than others). For example, I've experienced both huskies and rottweilers that like to "talk" when you pet them - meaning they moan and make strange noises out of being in a contented state of mind.