Starbase 36 was a United Federation of Planets facility active in the 23rd and 24th centuries. It was near Nimbus III and near both the Romulan Neutral Zone and the Organian Treaty Zone. (TNG: "The Mind's Eye")

United Federation of Planets starbases
Starbases: 1 - 2 - 3 - 4 - 5 - 6 - 7 - 9 - 10 - 11 - 12 - 14 - 15 - 16 - 17 - 18 - 20 - 21 - 22 - 23 - 24 - 25 - 26 - 27 - 28 - 29 - 30 - 31 - 32 - 33 - 36 - 37 - 38 - 39-Sierra - 41 - 42 - 43 - 44 - 45 - 47 - 47-Vanguard - 52 - 53 - 61 - 73 - 74 - 78 - 86 - 88 - 105 - 118 - 125 - 129 - 134 - 137 - 140 - 152 - 185 - 188 - 193 - 200 - 201 - 211 - 212 - 214 - 217 - 222 - 227 - 237 - 247 - 310 - 311 - 315 - 332 - 371 - 375 - 376 - 397 - 414 - 505 - 512 - 514 - 515 - 544 - 549 - 592 - 600 - 621 - 718 - 732 - 771 - 804 - 814 - 901 - Earhart - Expanse 3 - Expanse 4 - Expanse 7 - Expanse 12 - G-6 - Osiris - Pitcairn - Rockford - Unity 1 - Unity 2 - 001
Deep space stations: 1 - 2 - 3 - 4 - 5 - 6 - 7 - 9 - 9-II -10 - 12 - 14 - 17 - B-5 - K-1 - K-7 - K-12