More detail on the major branches

http://www.owlpages.info/downloads/A_Phylogenomic_Study_of_Birds_Reveals_Their_Evolutionary_History.pdf
"The largest clade in Neoaves was a well supported
land bird clade (green, node F, Fig. 2)
(3) that contained the Passeriformes (perching
birds, representing more than half of all avian
species), which is allied with several morphologically
diverse orders. These included Piciformes
(woodpeckers and allies), Falconiformes (hawks
and falcons), Strigiformes (owls), Coraciiformes
(kingfishers, hornbills, rollers, and allies), Psittaciformes
(parrots), Coliiformes (mousebirds), and
Trogoniformes (trogons). One of the most unexpected
findings was the sister relationship
between Passeriformes and Psittaciformes (node
A, Fig. 2), with Falconidae (falcons) sister to this
clade. This relationship varied slightly among
analyses and gene-jackknifing (Fig. 1), yet the
close relationship between passerines with parrots
and/or falcons appeared consistently.
Sister to the land birds is the Charadriiformes
(shorebirds, gulls, and alcids; yellow, node G,
Fig. 2). This grouping seems to be driven primarily
by the b-fibrinogen gene (FGB), because
it was present in analyses of only this gene and
disappeared when the gene was removed through
jackknifing (Fig. 1). Regardless of the exact
placement of the Charadriiformes in our analyses,
we consistently support that this order is not
basal within Neoaves (24) and thus refute the
hypothesis that transitional shorebirds gave rise
to allmodern birds (7). Our phylogeny revealed a
highly supported water bird clade (blue, node H,
Fig. 2) (3, 14), including members of the
Pelecaniformes (totipalmate birds), Ciconiiformes
(storks and allies), Procellariiformes (tubenosed
birds), Sphenisciformes (penguins), and
Gaviiformes (loons)."

But notice that they have lumped the shorebirds, gulls, and alcids together.