You need the first three elements to go into the first group, the next three to go into the second group, and so on. How would you write it?
groups[1], groups[2], groups[3] = items[i], items[i+1], items[i+2]
If the group count is dynamic, you can just loop over groups instead, and then step through items by #groups, inserting.
It's also worth noting your solution exhibits similar off-by-one behaviour. The left hand side constants (integer values) do not match the right. It's error prone.
>You can't add 1-based indices together like you can zero-based indices.