Neanderthal DNA - What Can We Infer About Neandertalian Society?

Neanderthal remains were found in a cave, dating back to between 59 and 51,000 years ago. They had high levels of background in breeding according to the DNA tests carried out on them. This is almost like a community - they don't maybe seem as well connected to one another as modern day hunter-gatherer societies that we have now.