What you're seeing is how cannas multiply, and yes, all the shoots are connected to a main rhizome. Personally, I like having the mass of several stalks and flowers in one pot and would just transplant it to a larger pot, or put it in the ground. The pot you planted in is too small.

What type canna is it?
Here's one I have in a pot.....
{{gwi:534001}}

wow, that's a beauty!
I don't know what kind mine is, I'll have to look at the label.
I can move it into a bigger pot, but I thought this pot was big enough, cuz I saw a neighbor who has about 10 cannas in pots that are smaller than mine.
Maybe he is planning to repot.

ellenr

Ellen,

I started out just like you. I had on rhizome planted in a VERY large yard. It started growing, multiplying. Think of them as freebees. I break them off at the tuber when they're just starting to grow and I plant elsewhere. Just be careful not to do this on a hot sunny day or the stress on the roots will cause the new plant's leaves to burn. If this happens, just keep in the garage or something for a couple of days until it strengthens out again