Hi Victor,
I'm sorry for the delay in responding; I just discovered that lmfdb-support emails were going to spam.
I'm certainly interested in adding this kind of data, though there are some constraints. I had seen the first subgroup database you mentioned, but was dissuaded by the fact that all of the data is in pdf form. Also, we want actual generators of the subgroup and not just the structure of the subgroup poset.
I think 657,007 is probably more subgroups than we want to add for a single group (we've usually limited to a few thousand, though this could be stretched for groups lik Sp(8,2) that are of more interest than a random group in the database). But I'd be interested in chatting about how we can incorporate some aspects of the computation. We're having an editorial meeting in a few days; let me get back to you after that.
David