I contacted some family members, and I got somemore info on Zychas: Here's a direct line of my ancestors on the Zycha side (in reverse chronological order):
Hildegund Zycha, *1948 Rastatt (Austria)
Walter Zycha, Diplom-Ingenieur, *1902 Vienna +1971 Mühldorf (Germany)
Adolf Zycha, Prof. jur., *1871 Vienna, +1948 Bonn
Josef (Joseph) Zycha, Gymnasialdirektor, k.k. Regierungsrat,*1843 Lipowa/Lipova (Moravia), +1918 Vienna
Johann (Jan) Zicha, Viertler, *1811 Lipova (Moravia) +?
Franz Zicha, Viertler, *1787 Lipova (Moravia), +?
Johann (Jan?) Zicha, Viertler, Lipova (Moravia) +?
So it seems that your Jan Zycha *1874 is either a son of Josef or some (other) grandson of Jan Zicha.
Nicolai Czempin
http://www.czempin.de/nicolai/blog/