Edit: Turns out I wasn't remembering correctly, the digital gadget department is big enough.
For example, Dongil is another big industrial, and engineering group coexisting completely in parallel to Samsung, but they been buying and selling businesses from Lee's family as far as record goes.
CJ is the largest producer of sugar and flour in Korea, and they also sell every kind of processed and frozen foods. They also own the largest courier service in Korea, the largest cinema chain and film studio, several restaurant and coffee brands, a chain of cosmetics stores, biomedical services, and a dozen cable channels. They literally supply the whole country with both panem and circenses, and they deliver to your doorstep. It's vertical integration at its finest.
Shinsegae is a retail giant. They own a chain of department stores as well as the e-mart shopping mall. The latter has sprouted its own chain of Costco-like discount stores and convenience stores.
If you ever wondered who owns the "CU" brand of convenience stores that are ubiquitous in Korea, they are in-laws of the founder of Samsung. The same family owns the JoongAng Ilbo newspaper, which together with the JTBC news channel comprise the second largest media conglomerate after CJ. Oh, and they also own the third largest cinema chain in Korea.
The Lee family is also into furniture, paper, you name it. They used to make cars and planes, too.
All these companies aren't always on friendly terms with one another, as some of them have split from Samsung decades ago and compete with one another. But together they control such a huge portion of the country's commerce, news, and entertainment that the phrase "Republic of Samsung" comes up whenever a member of the Lee family is accused of wrongdoing.