TOKYO—Toshiba Corp outlined plans on Friday to split into three companies in an attempt to appease activist shareholders calling for a radical overhaul of the Japanese conglomerate after years of scandals. A rare move in a country dominated by conglomerates, Toshiba’s breakup comes the same week U.S. industrial powerhouse General Electric called time on its sprawling empire and Johnson & Johnson announced it was splitting up too. Founded in 1875, Toshiba plans to house its energy and infrastructure divisions in one company while its hard disk drives and power semiconductor businesses will form the backbone of another. A third will manage Toshiba’s stake in flash-memory chip company Kioxia Holdings and other assets. The plan, borne of a five-month strategic review undertaken after a highly damaging corporate governance scandal, is partly designed to encourage activist shareholders to sell their stakes, sources with knowledge of the matter have said. A breakup, however, …