Iishi Shrine is the shrine that Jyufukuji was built as a Jinguji for. It is a very ancient and important shrine being listed in both the Izumo Fudoki and the Engi Shiki. The main kami is Iishitsuhenomikoto, otherwise known as Amenohinatori or Takehiratori.
The white fence behind the shrine surrounds a large rock, the goshinati of the shrine, and it was onto this rock that the kami descended. The rock itself is considered the honden. According to records from ancient Izumo, Takehiratori was the son of Amenohohi who was the first emissary sent by Amaterasu to convince Izumo to cede their land to the Yamato. According to the Yamato version of events in the Kojiki, Amenohohi sided with Okuninushi and did not get back in touch with the High Plain of Heaven, so they sent Takemikazuchi to convince Okuninushi. In the Izumo version however, Amenohohi did sent a message back and his son, Takehiratori descended and arranged the transfer of land, known as Kuniyuzuri.
The Nihon Shoki also says that Takehinatori came with divine treasures that were placed in the Izumo Grand Shrine which suggests that the records of Gakuenji that state Izumo Taisha enshrined Susano originally may have some credence. Both Amenohohi and Takehiratori are considered ancestors of priestly lineage that functioned as head priests of Izumo taisha as well as governors of Izumo.
There is a smaller secondary shrine within the grounds, Takuasha, that enshrines Kibitsuhiko.
What is also unusual about Iishi Shrine is that there are no komainu or shimenawa, in fact no "decoration" at all.