  In this work we study particular TQFTs in three dimensions, known as Symmetry
Topological Field Theories (or SymTFTs), to identify line defects of
two-dimensional CFTs arising from the compactification of 6d $(2,0)$ SCFTs on
4-manifolds $M_4$. The mapping class group of $M_4$ and the automorphism group
of the SymTFT switch between different absolute 2d theories or global variants.
Using the combined symmetries, we realize the topological defects in these
global variants. Our main example is $\mathbb{P}^1 \times \mathbb{P}^1$. For
$N$ M5-branes the corresponding 2d theory inherits $\mathbb{Z}_N$ $0$-form
symmetries from the SymTFT. We reproduce the orbifold groupoid for theories
with $\mathbb{Z}_N$ $0$-form symmetries and realize the duality defects at
fixed points of the coupling constant under elements of the mapping class
group. We also study other Hirzebruch surfaces, del Pezzo surfaces, as well as
the connected sum of $\mathbb{P}^1 \times \mathbb{P}^1$. We find a rich network
of global variants connected via automorphisms and realize more interesting
topological defects. Finally, we derive the SymTFT on more general 4-manifolds
and provide two examples.
