Compact families of noncompact subgroups and clopen partial orders

For a locally compact Hausdorff group \\(G\\), let \\(\\mathcal N(G)\\) be the space of closed noncompact subgroups with the full Vietoris topology. We prove that a compact Hausdorff space \\(X\\) embeds in some \\(\\mathcal N(G)\\) if and only if \\(X\\) admits a partial order with clopen principal ideals. In the affirmative case, \\(G\\) may be chosen to be the discrete abelian group \\(\\mathbb Z\\oplus\\bigoplus_X\\mathbb Z/2\\mathbb Z\\). The quotient of \\([0,\\omega_1]^2\\) obtained by collapsing its closed lower triangle is a scattered compact space that admits no such order. It therefore gives a negative answer to Kourovka Problem 9.47.