  The commuting conjugacy class graph of a non-abelian group $G$, denoted by
$\mathcal{CCC}(G)$, is a simple undirected graph whose vertex set is the set of
conjugacy classes of the non-central elements of $G$ and two distinct vertices
$x^G$ and $y^G$ are adjacent if there exists some elements $x' \in x^G$ and $y'
\in y^G$ such that $x'y' = y'x'$. In this paper we compute various spectra and
energies of commuting conjugacy class graph of the groups $D_{2n}, Q_{4m},
U_{(n, m)}, V_{8n}$ and $SD_{8n}$. Our computation shows that
$\mathcal{CCC}(G)$ is super integral for these groups. We compare various
energies and as a consequence it is observed that $\mathcal{CCC}(G)$ satisfy
E-LE Conjecture of Gutman et al. We also provide negative answer to a question
posed by Dutta et al. comparing Laplacian and Signless Laplacian energy.
Finally, we conclude this paper by characterizing the above mentioned groups
$G$ such that $\mathcal{CCC}(G)$ is hyperenergetic, L-hyperenergetic or
Q-hyperenergetic.
