Michael,
Unfortunately, this does not work this way. There are many other factors which are involved in the calculation for the premiums that you have to pay for insurance purposes. Things like where the car is going to be kept, number of miles you'll be doing, car security features etc all come into play. As you correctly said, quotes will vary from company to company and sometimes you can notice a huge difference in the price being quoted, hence I understand your confusion. However what you need to do is go on a car comparison site and check what premiums you're getting for your vehicle and forget about the car insurance groups because it's only an indication and nothing more. Expect to pay more as your car falls into the higher car insurance groups as opposed to the lower ones (Group 1-5).