Depends what you mean by "group-level". A large part of Dawkins was pointing out that many of your individual genes had a very large stake in wanting your nieces and nephews to survive, as there was a high probability those genes were also present in the niece and nephew.
Which is actually a pretty good reason for something like menopause to get programmed in. A proto-human capable of getting pregnant into her 60s would produce more offspring, but if accumulated damage meant they (and she) rarely survived the pregnancy, that could be less beneficial to the family group (including numerous relatives other than direct descendants) on average than having her switch the capability off and live another generation (but not many more generations, because then there's a lot of infertile people competing for food, and your tribe only needs so much accumulated wisdom)
Which is actually a pretty good reason for something like menopause to get programmed in. A proto-human capable of getting pregnant into her 60s would produce more offspring, but if accumulated damage meant they (and she) rarely survived the pregnancy, that could be less beneficial to the family group (including numerous relatives other than direct descendants) on average than having her switch the capability off and live another generation (but not many more generations, because then there's a lot of infertile people competing for food, and your tribe only needs so much accumulated wisdom)