More Holographic M5 branes in $AdS_7 \times S^4$

We study classical M5 brane solutions in the probe limit in the $AdS_7 \times S^4$ spacetime geometry with worldvolume 3-form flux. These solutions describe the holography of codimension-4 defects in the 6d boundary dual $\mathcal{N}=(0,2)$ supersymmetric gauge theories. Starting from some half-BPS solutions which follow stricter BPS conditions, we find a general $\frac{1}{16}$-BPS solution. We show how some of the \textit{giant-like} M5 brane solutions here may be related to the codimension-2 surface operators in the 4d gauge theory.