  M5 branes on a D-type ALE singularity display various phenomena that
introduce additional massless degrees of freedom. The M5 branes are known to
fractionate on a D-type singularity. Whenever two fractional M5 branes
coincide, tensionless strings arise. Therefore, these systems do not admit a
low-energy Lagrangian description. Focusing on the 6-dimensional N=(1,0)
world-volume theories on the M5 branes, the vacuum moduli space has two
branches were either the scalar fields in the tensor multiplet or the scalars
in the hypermultiplets acquire a non-trivial vacuum expectation value. As
suggested in previous work, the Higgs branch may change drastically whenever a
BPS-string becomes tensionless. Recently, magnetic quivers have been introduced
with the aim to capture all Higgs branches over any point of the tensor branch.
In this paper, the formalism is extended to Type IIA brane configurations
involving O6 planes. Since the 6d N=(1,0) theories are composed of
orthosymplectic gauge groups, the derivation rules for the magnetic quiver in
the presence of O6 planes have to be conjectured. This is achieved by analysing
the 6d theories for a single M5 brane on a D-type singularity and deriving the
magnetic quivers for the finite and infinite gauge coupling Higgs branch from a
brane configuration. The validity of the proposed derivation rules is
underpinned by deriving the associated Hasse diagram. For multiple M5 branes,
the approach of this paper provides magnetic quivers for all Higgs branches
over any point of the tensor branch. In particular, an interesting infinite
gauge coupling transition is found that is related to the SO(8) non-Higgsable
cluster.
