In this paper, we get the fact that the identity map of $SU(3)/T(k,l)$ which is a 7-dimensional non-symmetric normal homogeneous space is stable.
"Stability of the Identity Map of $SU(3)/T(k,l)$." Tokyo J. Math. 17 (2) 281 - 289, December 1994. https://doi.org/10.3836/tjm/1270127952