  We observe a correspondence between collections of closed subgroups and
normal subgroups in totally disconnected locally compact groups. This
correspondence is applied to prove structure theorems for two classes of
totally disconnected locally compact second countable groups: the class of such
groups with an open solvable subgroup and the class of such groups with a
pro-nilpotent compact open subgroup. As a second application, we give new
proofs and generalizations of results of G. Willis and Y. Barnea, M. Ershov,
and T. Weigel on totally disconnected locally compact groups which are
topologically simple and compactly generated,
