It's dependent on the capacity of the fleet. You probably have a maximum capacity of 12. The small ships, like the cutter, defender and gunboat take 3 capacity, so your maximum number of ships will then be 4. Research can improve the capacity (I think you have to look for "logistics" in one of the trees but I'm not sure).

I had some techs in that are. It seems not enough. Now I am at 6 ships.

There was a post earlier on the value of the size of ships which I think is in one of our Folders. Gunathor had posted what he found.

Tiny ships are 1

Small are 3

Medium are 5

large are 7

If you have the first 3 tiers of logistics I (THINK) including the one that opens for a +2 you will have 18?

So you can do (6 small) or (3 medium and 2 tiny) or (2 large and 1 medium). 

I am not 100% sure on the values for tiny and I may be really off. Hope this helps somewhat.