Dec 6 (Reuters) - U.S.-based hedge fund Engine Capital LP is pushing Kohl"s Corp (KSS.N) to consider a sale of the company or separate its e-commerce division to improve its lagging stock price. Engine Capital, which owns about 1% stake in Kohl"s, said on Monday the department store has underperformed both the S&P 500 and other retailers in recent years, despite its large retail footprint and real estate holdings. Shares of the company, which were up about 4% on the news, have risen about 19% this year, while peer Macy"s Inc (M.N) has more than doubled. The S&P 500 index (.SPX) is up nearly 21% in 2021. The New York-based hedge fund added that Kohl"s should consider a strategic review of the whole company, including a sale, adding that it believes there are sponsors that would pay at least $75 per share or a 50% premium. Engine Capital, known for being instrumental in a $2 billion sale of Ann Taylor brand parent Ann Inc in 2015, said Kohl"s e-commerce business alone could be worth $12.4 billion or more. Kohl"s in response said the company continues to examine all opportunities for maximizing shareholder value. Engine Capital"s proposal comes at a time when retailers have doubled down on their online businesses following the e-commerce boom during the COVID-19 pandemic that drove people to shop online as they avoided crowds at brick-and-mortar stores. Last month, Macy"s Inc (M.N) said it was working with consulting firm AlixPartners after activist investor Jana Partners pushed for a sale of its digital business, while Hudson"s Bay Co-owned Saks Fifth Avenue has said it would spin off its e-commerce segment. read moreEarlier this year, Kohl"s also faced pressure from a group of activist investors to add board members with retail experience, following which it added three new directors. read more