I have been in this situation a lot, particularly in my last master year, where group projects were literally piling up.
One thing you need to understand is that, in any group work (at school or at work), there will always be people working more than others, and everyone will get the reward. Why? Because in a project, what matters is the completion of the project, not of your part.
I suspect my own professors tried to teach us this lesson, because I know other students who reported the kind of issue you report, and noone did anything, in fact the projects that were unfinished were still blamed: if a project fails, no matter why, it's the whole group's fault, you included even if you did your part of the work.
Indeed: why assign a group project when you can have individual assignments? This might beserve to enforce training in group work. And group work's goal is to not only do your part of the job, but working together to complete the whole work. Managing dissensions and colleagues not working enough is unfortunately part of any group work, so you have to know how to handle it.
Concretely, I think two ways to approach this, depending on your objectives:
Report it to those in charge: this might (but not necessarily) get you sole credit for the project and punish your colleagues. Ideally, this is only fair to do that. Downside is that if the professors wanted to get you to train in group work, you will clearly show you failed, and also probably you won't get a good mark if the group work is unfinished (even if you completed your part: what matters is the project, not what you did).
Let it slide and do all the work yourself: if you are interested in having good marks, this is the best way to go. Downside is that you might have a LOT of work to do, but the bright side is that you can ensure the work is done well, and you can show off as the one presenting theshine during project to the professorspresentation (if you have one scheduled), knowing your project better than anyone else. So even if you let it slide, you can show you did most of the work without telling it directly, which is way more appreciated by everyone (both your colleagues, professors and superiors in a professional setting). Another advantage is that you will get a lot of skills in a short period of time (at the expense of sleep...).
Also, there is a 3rd way: balancing the work. Often, students have different skills and they do not necessarily excel for all kinds of projects. If you have several projects, what you can do is that you can arrange with your colleagues to form the same team in different projects, and share the work depending on each member's skills and affinities: you might end up doing most of the work for project A, but one of your colleague will do most of project B since he is more skilled with working on B field, etc.
The only requirement for this 3rd way is that you choose colleagues that are able, and that you upfront discuss and concur on this solution (if you discuss later on in the project, it might not end well as you experienced...). If you have lots of projects, this might actually help you speed up the completion, by assigning adequately to the most pertinent member the work to be done. And bonus, this is what a good manager should do, so that's also a good training if you want to lead projects later on :-)