In the present paper, a weak form of sandwich classification for the overgroups of the subsystem subgroup
E
(
Δ
,
R
)
E(\Delta ,R)
of the Chevalley group
G
(
Φ
,
R
)
G(\Phi ,R)
is proved in the case where
Φ
\Phi
is a simply laced root system and
Δ
\Delta
is its sufficiently large subsystem. Namely, it is shown that, for such an overgroup
H
H
, there exists a unique net of ideals
σ
\sigma
of the ring
R
R
such that
E
(
Φ
,
Δ
,
R
,
σ
)
≤
H
≤
Stab
G
(
Φ
,
R
)
(
L
(
σ
)
)
E(\Phi ,\Delta ,R,\sigma )\le H\le \operatorname {Stab}_{G(\Phi ,R)}(L(\sigma ))
, where
E
(
Φ
,
Δ
,
R
,
σ
)
E(\Phi ,\Delta ,R,\sigma )
is an elementary subgroup associated with the net and
L
(
σ
)
L(\sigma )
is the corresponding subalgebra of the Chevalley Lie algebra.