Initially Somogi worked as a piano teacher before joining the New York City Opera.

Between seasons Somogi worked as an assistant conductor to Thomas Schippers in Italy at the Spoleto Festival and to and Leopold Stokowski in New York at the American Symphony Orchestra.

From 1977 to 1980, Somogi served as music director of the Utica Symphony Orchestra, making her the first woman to hold a permanent orchestral post in the United States.

Somogi also conducted the Oklahoma City Orchestra and the Tulsa Philharmonic.

Poor health caused her to retire in 1987 and she died in Long Island, in 1988 after a four year battle with cancer.