How do I combine three or more standar deviations?

Question

I am trying to compare some results in different experiments by using meta-analysis. Each study involved has a different number of subgroups. Since only mean and standard deviation is available for each subgroup, then an option to deal with is to combine the known parameters in each study (e.g. mean, standard deviation). In some books appear how to do it for two groups but my questions is How to combine three or more standard deviations. Thanks in advance.