First, as the other answer said too, be "very" careful if this is allowed. Probably it isn't - if a client is so important that the companies existance depends it, it is a good hint that you're really being an employee, not a consultant.
And other than fines, it might happen that the company must retrospectively pay taxes etc. for you without you getting back the same taxes (meaning, paid two times). This can hurt much more than the fine.
Anyways, some stuff about taxes etc. (very rough estimation, and many small things not mentioned at all):
Currently, you have 52000 per year on your payslip as "gross" (not really) salary, which makes about 3700 14 times. After insurance and Lst tax, this might be eg. 34000, ie. 2350 14 times (nice - there are more and more web developers getting maybe half of it).
However, because many people are just not aware of it, this "gross" isn't really gross - the employer has additional costs which are hidden to you, namely your insurance again (about half, while you see just the other half), and some other taxes and fees. Including this, your gross salary is more like 68000. If you are self-employed, you've to care about this previously hidden part too.
Since you want "significantly" more, how about 2700 instead of 2350 - this would be instead 81000 instead of 68000 gross-gross per year.
Then ... while Lst and insurance calculation are not that different between self-employed and not, there is also the Umsatzsteuer, 20%. Makes 97000.
Since this is yearly, the missing 13+14 month are already in there. Not in there are the missing 25 vacation days, and average 13 (?) sick days. Since without weekends, national holidays, etc., there are about 245 days per year, this 38 days are about 15% which you get not paid anymore as self-employer person. This added makes 112000.
Some random small fees collectively considered with 6% (house number, may vary), 119000.
(Already more than double, compared to your payslip gross value).
To this, add tax consultant, legal expense insurance, costs for computer stuff (hardware, software, server rent, redundant backups, etc.etc.), and of course office space (including rent, cleaning, furniture, electrity, garbage fee, etc.etc. - all of this is also relevant for home office, just not directly on an separate invoice. Also multiply this part with ca. 1.1 because tax details).
What you have now would be what you need/want per year - however, you're not earning money for 8 hours a day over the whole year. The last big point is, enough overhead on your hourly rate to live through times without work as well as non-billable work.