Thank you for the additional information.
So, narrowed down, what you want is one coach for 14 days to start and return to Prague.
You will need a Czech driver and coach which is authorised to drive in Poland, Hungary, Croatia and Austria, and other countries you will transit without stopping.
You have already calculated that you will be driving a minimum of 2500 km, and that all that driving will be on the 6 transit days, so that the 28 hours of driving divided by the 6 days gives an average of 5 hours driving plus 2 x 30 minutes mandatory rest stops gives an average of 6 hours driving each driving day.
I don't have the answers of who is reputable in Prague to hire a coach for 2 weeks with 2 drivers (who will also need their days off during the trip so you will need to allow for that) nor how to know if they are reputable and safe - you will need to do some work on that yourself - nor how much that will cost plus tolls plus fuel plus hotels for the drivers plus food for the drivers. I expect it will be quite expensive, but perhaps spread over 14 people it won't seem so bad.
I wouldn't expect them to speak English or any of the Indian languages. Do you have Czech speakers in your group?