A variety
V
\mathbf {V}
is group universal if every group
G
G
is isomorphic to the automorphism group
Aut
(
A
)
{\operatorname {Aut}}(A)
of an algebra
A
∈
V
A \in \mathbf {V}
; if, in addition, all finite groups are thus representable by finite algebras from
V
\mathbf {V}
, the variety
V
\mathbf {V}
is said to be finitely group universal. We show that finitely group universal varieties of Heyting algebras are exactly the varieties which are not generated by chains, and that a chain-generated variety
V
\mathbf {V}
is group universal just when it contains a four-element chain. Furthermore, we show that a variety
V
\mathbf {V}
of Heyting algebras is group universal whenever the cyclic group of order three occurs as the automorphism group of some
A
∈
V
A \in \mathbf {V}
. The results are sharp in the sense that, for every group universal variety and for every group
G
G
, there is a proper class of pairwise nonisomorphic Heyting algebras
A
∈
V
A \in \mathbf {V}
for which
Aut
(
A
)
≅
G
{\operatorname {Aut}}(A) \cong G
.