The amiral spaceship goes with the hero, there can only be a single one of a single type of those in a raid.
To get points for your hero, potential objects and all that stuff, you will have to make sure that the spaceship is not destroyed in a raid. Make him stand back, behind the rest of your fleet.
You will get new spaceships as soon as your hero is upgraded and has a higher level.
Go in “Amiral ships” (vaisseaux amiraux), to see all the ships possible.
You will have the ship, its name, its effects and its level. You'll probably notice that it is possible to up the level of the amiral ship to increase its effects. To do so, you will have to spend some resources.
Some ships have a little box on the right with some squares, they are peaces of maps, and you can be these by clicking on the square (against some dark matter) or you can find them when raiding someone.
For the tortle, deux of the maps can not be bought, you'll have to find them.
To improve your ship, you will need resources and all the maps. For each level you will need new maps.
If you have the needed resources but the “Improve the ship” button does not appear, it means you are missing some maps.