Hey!

A marks of 578 will fetch you a rank between 13064-16008. You can check it here

Although it is quite difficult to predict that  whether you will get seat or not as cut off marks for medical colleges keeps changing every year but when we go through previous data then it suggests that with 578 marks and 3B category you have chances of getting a government medical in Karnataka. Since you didn't mention the subcategory of 3B, I am mentioning the cut off all 3B categories.

Last year the first round closed at 73870 for category 3BG

And for category 3BK the first round closed at 120807 and 3BR closed at 93000.

You can check the list of colleges in which you have chances, you can use the NEET college predictor here