Since you are talking about NIT and IIT's so its obvious cutoffs and ranking would be high.

Now coming to your question, as you have not mentioned your state quota or something else so am considering your rank as AIR. So with sc category rank 66407, I am bound to say that you will not get any NIT and in case of IIT you have to appear in JEE Advanced, provided you fulfill the eligibility criteria for JEE Advanced. For more information regarding this you may visit to JOSAA official site.

You may also check the different NITs cutoff for CSE branch through this link: https://engineering.careers360.com/articles/nits-cutoff-for-top-btech-branches

In case you need to check the different IITs cutoff for CSE branch, you may refer to this link: https://engineering.careers360.com/articles/jee-main-cutoff-for-top-iiits

And you can also check the best college for yourself on the basis of your rank by using the college predictor tool, link is here: https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer

All the best!!

Hello aspirant

Congratulations for getting  66407 category rank in jee main. Its very hard to give exact chance of admission in a college as cutoff of college vary every year based on different factor. One can predict chance of getting in a college by analysing past year trends.

Factor affecting cutoff -

1. No of students

2. No of seats

3. Difficulty of paper

4. past year trends

5. Home state

If you are from Delhi

College you will get seat in cse branch.

1. Iiit Delhi

You can get other branches in

1. Iiit pune
2.dtu

You can choose best college according to your rank using careers360 college predictor tool

https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer

Hope this will help

Best of luck