Let
G
\mathbf {G}
be a split classical group over a non-Archimedean local field
F
F
with the cardinality of the residue field
q
F
>
5
q_F>5
. Let
M
M
be the group of
F
F
-points of a Levi factor of a proper
F
F
-parabolic subgroup of
G
\mathbf {G}
. Let
[
M
,
σ
M
]
M
[M, \sigma _M]_M
be an inertial class such that
σ
M
\sigma _M
contains a depth-zero Moy–Prasad type of the form
(
K
M
,
τ
M
)
(K_M, \tau _M)
, where
K
M
K_M
is a hyperspecial maximal compact subgroup of
M
M
. Let
K
K
be a hyperspecial maximal compact subgroup of
G
(
F
)
\mathbf {G}(F)
such that
K
K
contains
K
M
K_M
. In this article, we classify
s
\mathfrak {s}
-typical representations of
K
K
. In particular, we show that the
s
\mathfrak {s}
-typical representations of
K
K
are precisely the irreducible subrepresentations of
ind
J
K
λ
\operatorname {ind}_J^K\lambda
, where
(
J
,
λ
)
(J, \lambda )
is a level-zero
G
G
-cover of
(
K
∩
M
,
τ
M
)
(K\cap M, \tau _M)
.