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The issue of extracting guided modes from a standard light-emitting heterostructure similar to those of visible or near-infrared light-emitting diodes is considered with respect to the role of lattices and of the amount of omnidirectionality in the extraction performances. Triangular lattices are first-order natural candidates. We examine first whether they can be made omnidirectional thanks to a grating + coupler combination initially proposed by Fehrembach et al (2001), whereby the short periodicity concentrates emission in few in-plane modes, and the double periodicity extracts it. We then examine lattices that directly extract, for a Ga(Al)As system on a GaAs substrate, with a specific 3-D mode decay calculation. We compare triangular and Archimedean lattices experimentally and point out the role of photonic strength also through a spectrally and angularly resolved experiment.