Neuroptera: Lacewings, Antlions, Owlflies, et al
The two large, membranous wings of these insects are usually held "roof-like over the body" (Castner p. 107), and the wings have both many longitudinal veins and many cross veins (hence, lit. "nerve-winged"). They have long and variable antennae (see the image here). This Insect Order includes Suborders Raphidiodea (Snakeflies) and Planipennia (Lacewings, Mantispids, Antlions, and Owlflies).
Owlflies (Suborder Planipennia, Family Ascalaphidae)
(Click on each image to enlarge it.) Owlflies are Dragonfly-like in appearance (both having bulging eyes, similar-looking wings, and elongated bodies), but may readily be distinguished from the latter by their long, knobbed antennae (Dragonfly antennae are "small and bristle-like [setaceous]", says Castner on page 55), and by their outstretched wings while resting. Note also the fuzzy structures on the underside of the thorax in the image above right, which are absent in Dragonflies.
The Owlfly pictured above appears to be of the Ascalaphinae Subfamily -- the one with bisected eyes, which typically occupies "grasslands and warm dry woodlands" (Resh & Carde p. 792). Most species of Owlfly are nocturnal or crepuscular, and fly like Dragonflies (but are not similarly dependent on water). They catch their insect prey on the fly. The predacious larvae live in the ground litter, and pupate there in silken cocoons.
Owflies are closely related to Antlions (Family Myrmeleontidae).