Grass radical on top marks 菊 as a plant - chrysanthemum is one of the four classical noble flowers (mei, lan, zhu, ju) and the radical places it firmly in the floral family alongside 花, 莲, 兰, 茶.
匊 supplies the sound - jū drifting tonally to jú. The graph pictures a hand 勹 cupping grains 米, originally a handful scooped up. It adds a faint visual flavour: a chrysanthemum has tightly packed petals like grains in a cupped palm. Same phonetic in 鞠 bow, 掬 scoop.
