I'll address the final version of the question, which is much more coherent. The most important improvement that I suggest is providing context on what Google Groups is or does. This seems nit-picky, but it's a pain in the neck for us to have to figure out legally irrelevant technical details. Tell us what "moderation" means in this context (hint: SE moderation is not a "submit and await approval model. Tell us the facts that we need to know). I will stipulate for the sake of making the point that GG uses a pre-approval model where no post is distributed until an authorized human presses approve, at which point the emails are launched. That means that bad content is disseminated with your knowing and willful participation, and you cannot hide behind the defense "We didn't know this guy was making defamatory statements / distributing porn / inciting insurrection". Yes, you are liable. OTOH under the decades-old usenet automatic redistribution model (for alt), it's not even possible to moderate. Surely you can see how the correctness of my stipulations about the technology impinges on the correctness of any answer. Don't make us do your elementary non-legal research.
One sub-question here is whether contract law and the GG terms of service requires anything. You have to do the heavy lifting in tracking down the Google requirements – what did you agree to when you created the group? Did you read the TOS, does it say anything about moderation? Please note that the TOS is country specific and 99.99999% of active users on Law SE are not located in India, so we have no access to your TOS.
The second question is India-specific: is there any law of India that makes you do things not already required by Google? Given the nature of Indian law, you may have to be state-specific, and don't bother asking about Jammu and Kashmir, nobody knows. AFAIK, the India-specific content is mostly null, except for possible personal liability for disseminating locally-illegal content.
The addressable legal content of the final version of the question is, simply, "Are we (jointly or severally) liable for content distributed by members?". Normally, liability has to do with courts making you pay for your bad deeds. I suspect that most of the legal consequences of bad-content dissemination are implemented via Google policy. They will shut you down and ban you if you are bad enough. Police involvement is possible in the case of violation of child-porn or sedition laws. If you include "can Google shut us down", there are very many things that they can shut you down for. If you mean "can the police come after us", there are fewer grounds, but not none. If you mean "can we end up as parties in a civil suit because of stuff distributed via the group", that's probably even broader than the question of Google shutting you down (their TOS is designed to minimize their liability, your exposure is even greater).
The final version is a bit unfocused and in terms of scope is too broad, and I would delete "forcefully" because I don't know what that means, and it just confuses the question. But lacking access to the Indian TOS, it's also unanswerable. The earlier versions are incoherent (bad formatting, spelling, grammar, thematically all over the map). Note that your meta question right here has similar problems.