Let's have a centrally symmetric undirected graph $G$. For each edge $e$, we define a new graph $H_{e}$, which subdivides the edge $e$ in graph $G$. There is an automorphism on these new graphs, which defines $n$ equivalence classes.
Does that mean, there are always ${{\mid equivalenceClasses \mid}\choose{2}}$ pairwise non-isomorphic graphs, or do I have to check between each of the ${{\mid equivalenceClasses \mid}\choose{2}}$ class pairs, if $H_{e1}$ and $H_{e2}$ are isomorphic for an arbitrary $H_{e1} \in class1$ and $H_{e2} \in class2$?
These are completely equivalent notions; two graphs $H_{1}$ and $H_{2}$ are isomorphic if and only if there is an automorphism of $H_{1} \cup H_{2}$ interchanging $H_{1}$ and $H_{2}$.
Note that this means, using the approach you are suggesting, you are forming all of the graphs $H_{e}$ for each edge $e$ in $G$, then computing the automorphism group of $\cup_{e \in G} H_{e}$, which has $h(v+1)$ vertices (where $h$ is the number of edges of $G$, and $v$ is the number of vertices); this is a VERY big graph in general, and it will not be easy to compute it's automorphism group. You are probably better off pairwise testing isomorphism between the graphs (if you do this in a clever way you will most likely not have to test all pairs).