Each element exists in a group and there are just over 20 groups.
You start with 4 groups since you have the 4 basic elements
As you combine elements you'll eventually unlock more groups. Here's the remaining ones and an example of how to get them in no particular order:
Animals - Example: Air + Egg = Bird
Energy - Example - Air + Fire = Energy
Humans - Example: Golem + Life = Human
Materials - Example: Clay + Fire = Bricks
Organisms - Example: Life + Swamp = Bacteria
Plants - Example: Earth + Moss = Plant
Resources - Example: Domestic Animal + Human = Wool (and meat and blood)
Supernatural - Example: Ash + Life = Ghost
Tools - Example: Human + Metal = Tools
Transportation - Example: Wheel + Wheel = Transportation
There are other groups in the other episodes as well. These are just the basic ones.
Also check out this solution which is for the original Doodle God game on WP. It has a link to the full list of element combinations