Neanderthals and ancient ancestors of modern humans were probably far more promiscuous than we are today. How do we know? Because their fingers were shorter than ours are.
Androgens are the hormones that collectively affect the development of masculine traits in both males and females. They are also thought to affect how long people's fingers are, particularly the ratio between the index and ring fingers. If androgen levels are high, the ring finger will be longer relative to the index finger. The lower the ratio between index and ring finger, the higher the levels of androgens and, by extension, aggression.
This basic idea has led to a lot of potential correlations between finger length ratios and just about everything, ranging from one's risk of autism or schizophrenia to a person's personality and sexual orientation. A lot of these studies have been overhyped or misreported - in particular, there's apparently no link at all between digit ratio and male sexual orientation, although there does seem to be a correlation for women.
So, while it's pure pseudoscience to say you can deduce anything about a specific person from the lengths of his or her fingers, there are some things you can say about large groups of people based on these ratios, and that's where Neanderthals enter the picture. According to Emma Nelson, a researcher at the University of Liverpool, Neanderthals and a pair of early hominids, Ardipithecus ramidus and Australopithecus afarensis had much lower digit ratios than modern humans.
That means they likely experienced high levels of androgens in the womb, which likely had a significant effect on the population as a whole. Neanderthals would have been much more competitive and promiscuous than humans today. They found similar results for early modern humans and the much more ancient Ardipithecus. Interestingly, Australopithecus, which dates back to about 3 million years ago and so slots in between Ardipithecus and early modern humans, had slightly more modern ratios and so were more likely to be monogamous.
Nelson and her colleagues acknowledge that their findings are still preliminary, but these unlikely approaches may offer us the best chance to understand how extinct hominids interacted socially, particularly when there's no chance of finding more orthodox sources of information on the topic:
"It is believed that prenatal androgens affect the genes responsible for the development of fingers, toes and the reproductive system. We have recently shown that promiscuous primate species have low index to ring finger ratios, while monogamous species have high ratios. We used this information to estimate the social behaviour of extinct apes and hominins. Although the fossil record is limited for this period, and more fossils are needed to confirm our findings, this method could prove to be an exciting new way of understanding how our social behavior has evolved."