  We investigate the poset (P(X),\subset), where P(X) is the set of isomorphic
suborders of a countable ultrahomogeneous partial order X. For X different from
(resp. equal to) a countable antichain the order types of maximal chains in
(P(X)\cup \{\emptyset \},\subset) are characterized as the order types of
compact (resp. compact and nowhere dense) sets of reals having the minimum
non-isolated.
