At age 65 you are eligible for Medicare Part A (hospital), Part B (outpatient) and Part D (drug) benefits. If you are still working, you can select to sign up for only Part A (no premium if you have already contributed through work) and delay your Part B (premium based on income) because you have group health coverage. You do want to confirm with your group health plan that your drug benefits under the group plan are comparable to a Part D plan so that you do not incur a penalty under Medicare. If your company has less than 20 employees, Medicare would be your primary and the group plan becomes the secondary insurer.
Your initial enrollment period with Medicare when turning age 65 is the 3 months preceding your birthday month, the month of your birthday, and the 3 months following your birthday. I suggest to my clients that they contact (via phone or on www.socialsecurity.gov) Social Security the 4th month before their birthday to take care of their enrollment needs.