  We undertake a study of the conditional mean dimensions for a factor map
between continuous actions of a sofic group on two compact metrizable spaces.
When the group is infinitely amenable, all these concepts recover as the
conditional mean dimensions introduced in \cite{L22}. A range of results
established for actions of amenable groups are extended to the sofic framework.
  Additionally, our exploration encompasses the study of the relative mean
dimension introduced by Tsukamoto, shedding light on its inherent correlation
with the conditional metric mean dimension within the sofic context. A lower
bound on the conditional metric mean dimension, originally proposed by
Shi-Tsukamoto, is extended to the sofic case.
