Let $G$ be a group. Recall that a group $H$ is called a retract of $G$ if there exist  homomorphisms $g:G\longrightarrow{H}$ and $f:H\longrightarrow G$ so that $g\circ f=id_H$.  The homomorphism $g$ is called a retraction.     

My question is that:
  
Is there an infinite sequence $\{ H_i \}_{i\in \mathbb{N}}$ of groups so that the following conditions hold?     

1- $H_1$ is a finitely presented group.  

2- $H_{i+1}$ is retract of $H_i$ with the retraction $g_{i}:H_i \longrightarrow H_{i+1}$,  for all $i\geq 1$;    
  
3- $g_i$ is not an isomorphism for all $i\geq 1$.  
  
Thanks in advance.