Score dropped by 74 points after taking out a new credit card - What to do?

Too many inquiries within a shop period may drop your credit score. However, get your free credit report and check thoroughly.

Usually, your credit score won't drop by so many points just for taking out a credit card. Did you apply for too many credit cards at the same time?
It is better you pull your credit reports and check for errors. Dispute errors if any.

To protect your credit score from falling down, it's important to pay your accounts timely. Did you ever fall behind on your payments?
It is possible that your account was sent for collections and included on your credit report. Once it happens on your credit report, it will surely cause a drop in your credit score.

I agree with Good Nelly and Patricia, you somehow made few wrong moves which might have backfired.

Did you use your other credit cards too much? Your credit score might have dropped due to an increased utilization ratio. The ratio is an image of how much credit you're using by dividing your total credit card balance by your total credit limit.

Did you close any old credit card account that is in good standing? Did you settle any debt recently? This may be a reason.