I'm thinking that it should go under academic or other club/activity, but I'm kind of hesitant because there are also other aspects involved, such as community service.
How you classify your activities is completely up to you. I put NHS as community service even though it would fit in multiple spots. If you have another activity that is classified as community service, put NHS as academic or other club/activity. If you have an activity classified as academic, put NHS under community service or other club/activity. If you have an activity classified as other club/activity, put NHS under academic or community service. That way it shows that you have more of a variety of activities. Or if you want to show your dedication to one of those classifications (with 3+ activities in one classification) then put it there.
I'd say put it as community service, because (at least at my school) that's the focus. However, if a lot of your other activities are listed as community service, you might want to use the academic/other category. Either works, though! Just another option, you could put NHS under Honors/Awards if you need to save Activities space or fill Honors/Awards space. Hope this helps!
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Agree also the description of what you do matters not the catergory.