With a rank of 6,379 in the VIT Integrated M.Tech program, securing a seat in the Computer Science and Engineering (CSE) group at VIT Chennai could be challenging but not impossible. Here's a breakdown of the situation:

1. Previous Year Cutoffs : Admission to the CSE group, especially at VIT Chennai, tends to be highly competitive due to the high demand for the program. Historically, the cutoffs for CSE are higher compared to other branches. Reviewing the previous years' cutoff ranks for the CSE program can give you an idea of your chances.

2. Rank Analysis : A rank of 6,379 is generally considered higher in the context of a highly competitive program like CSE. In previous years, the cutoffs for the CSE branch have been significantly lower, especially for top ranks. However, if there are vacant seats or if the demand is lower than usual, there could still be a possibility.

3. Other Factors : Sometimes, the cutoff ranks can vary based on the number of applicants, seat availability, and other factors. If you are interested in VIT Chennai, participating actively in the counseling process and exploring other branches or specializations might also be beneficial.

4. Alternate Options : If you don’t secure a seat in CSE, consider exploring other branches within VIT or at other reputable institutions.

In summary, while your rank is on the higher side for CSE, there's still a chance, particularly if there are any changes in cutoff trends. Stay engaged in the counseling process and explore all options available to you.