Hello! I'm an urban entomologist at Cornell stationed here in Suffolk County. Your picture looks very much like a cockroach but I can't tell you what species. I can say it is likely that the roach either came up through the septic system OR it is a Pennsylvania woods roach, which is nothing to worry about since they don't live indoors. If you find another one like it inside a drain or near plumbing, it would be an Oriental cockroach, which are ubiquitous through sewer systems on Long Island. In that case, you might consider calling a plumber to see how your plumbing could be modified to block something like this. They normally can't come up through plumbing because there's a "J" shaped water-filled pipe under each sink, shower and toilet that prevents sewer smells and insects from coming up. 

Please let me know if I can help any further.

Thank you so much! 

Aahhh! Yes, definitely Oriental roaches. They have naturalized here in spots on Long Island! If you live anywhere near North Merrick schools, they have these guys on their campus and in the summer they are easy to find especially on the side of brick buildings. Basically outside they are harmless and they really don't want to be inside, unless there's a cool dark and wet place to hang out.

I'm glad I could help!