As with many other such moves Maytag bought Amana in 2001 from Goodman Appliances to strengthen their product line, in particular refrigerators. Barely five years later Whirlpool bought Maytag so that was that.
https://khak.com/whirlpool-plant-in-middle-amana-has-been-sold/
https://www.deseret.com/2001/6/5/19589812/maytag-corp-to-purchase-amana-for-325-million
Again buying a competitor to get at their technology or whatever goes way back. General Electric nabbed Hotpoint in part to get at patents and other technology for Calrod heating elements.
Over years it became an increasing demand from appliance dealers, housewives and others for appliance makers to have an entire breath of major appliance offerings; range/stoves/ovens, refrigerators/freezers, washing machines, dryers, dishwashers, etc...
Building new plants is expensive, and you might still not be able to produce what your competitor offers due to patents. Buying said competitor solves that problem.
For hot minute Maytag remained alive as an independent company Amana-Speed Queen continued to be built where they always had. This allowed Maytag to keep their prime "Dependable Care" and other lines under that brand, but offer market something else with Amana. That is Maytag laundry appliances were not supposed to be in direct competition to Amana.
https://www.automaticwasher.org/cgi-bin/TD/TD-VIEWTHREAD.cgi?74873_3
https://www.automaticwasher.org/cgi-bin/TD/TD-VIEWTHREAD.cgi?58683
Admiral was more of the same...
Magic Chef was well known for their range/ovens/stoves etc.. They were bought by Admiral who was known basically for refrigerators and freezers. Maytag bought Magic Chef so they got Admiral.
https://en.wikipedia.org/wiki/Magic_Chef
Maytag really never built anything else but laundry appliances, but by 1950's and certainly into 1960's full line appliance makers (Whirlpool, GE, Frigidaire) were starting to challenge Maytag's then near dominance of domestic laundry market.
Maytag did produce refrigerators, ovens, ironers and other things 1950's, but these were all sourced from others, and by 1960 Maytag stopped those limited efforts to concentrate mostly on laundry (domestic and commercial) appliances. This was not to be and didn't last.
By 1970's Maytag finally brought out their own designed and built line of dishwashers. It was late to market by then since GE, WP and Frigidaire long had such offerings.