  The symmetry operators generating the hidden $\mathbb{Z}_2$ symmetry of the
asymmetric quantum Rabi model (AQRM) at bias $\epsilon \in
\frac{1}{2}\mathbb{Z}$ have recently been constructed by V. V. Mangazeev et al.
[J. Phys. A: Math. Theor. 54 12LT01 (2021)]. We start with this result to
determine symmetry operators for the $N$-qubit generalisation of the AQRM, also
known as the biased Dicke model, at special biases. We also prove for general
$N$ that the symmetry operators, which commute with the Hamiltonian of the
biased Dicke model, generate a $\mathbb{Z}_2$ symmetry.
