This paper investigates the relationship between the p-length,
l
p
(
G
)
{l_p}(G)
, of the finite p-solvable group G and the number,
a
p
(
G
)
{a_p}(G)
, of orbits in which the subgroups of order p are permuted by the automorphism group of G. If
p
>
2
p > 2
and
a
p
(
G
)
≦
2
{a_p}(G) \leqq 2
, it is shown that
l
p
(
G
)
≦
a
p
(
G
)
{l_p}(G) \leqq {a_p}(G)
. If
p
=
2
p = 2
and
a
2
(
G
)
=
1
{a_2}(G) = 1
, it is proved that either
l
p
(
G
)
≦
a
p
(
G
)
{l_p}(G) \leqq {a_p}(G)
or
G
/
O
2
′
(
G
)
G/{O_{2’}}(G)
is a specific group of order 48.