館 is built from the 食, 宀 (roof), and 㠯 (with (in 官·追)) components.
It belongs to a phonetic family with 官 and 管 — they share the 㠯 component and the reading カン.
A common word using 館 is 映画館 (えいがかん), meaning “movie theater, cinema”.
Kanji that look similar include 餓.