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Apr 18, 2021 at 10:49 comment added IJL Yes, either $\mathbb{Z}_2*\mathbb{Z}_2*\mathbb{Z}_2$ or $\mathbb{Z}_2*\mathbb{Z}_n$ for any $n>2$ will do.
Apr 17, 2021 at 7:21 comment added JP McCarthy point 37, p.66 of Topics in Geometric Group Theory By Pierre de la Harpe tinyurl.com/ahzwd8ph suggests we only need $\mathbb{Z}_2\ast \mathbb{Z}_3$.
Apr 16, 2021 at 18:10 comment added YCor The last paragraph needs some elaboration. Indeed if $G\subset F_2/N$ and $F_2\subset H$ with $H$ free product of three cyclic groups of order 2 ($F_2$ has index 2 in $H$), $N$ is possibly not normal in $H$.
Apr 16, 2021 at 11:48 history answered IJL CC BY-SA 4.0