Lewis & Short

Ōgyges, is, Ōgygus, i, and Ōgy-gĭus, ĭi, m., = Ὠγύγης, Ὤγυγος, Ὠγύγιος, the mythic founder and king of Thebes, in Bœtia, in whose reign a great deluge is said to have occurred: oppidum Thebae, quod rex Ogyges aedificarit, Varr. R. R. 2, 1, 2: ante cataclysmon Ogygi, id. ib. § 3: hoc factum Ogyge rege dicebant, Varr. Fragm. ap. Aug. Civ. Dei, 21, 8.
Form Ogygus, Paul. ex Fest. p. 179 Müll.
Form Ogygius, Aug. Civ. Dei, 18, 8.
Hence,

  1. A. Ōgygĭ-dae, ārum, m., the descendants of Ogyges, poet. for the Thebans, Stat. Th. 2, 586.
  2. B. Ōgygĭus, a, um, adj., = Ὠγύγιος, Ogygian, poet. for Theban: deus, i. e. Bacchus, who was especially honored at Thebes, Ov. H. 10, 48; also, Lyaeus, Luc. 1, 675: populus, the Thebans, Sen. Oedip. 589: chelys, i. e. of Amphion, king of Thebes, Sid. Carm. 16, 3: Ogygia moenia, i. e. Thebae, Paul. ex Fest. p. 178 Müll.