This page indicates that the first two days is "very early" for a zygote to split, and that conjoined twins are the result of an "extremely late" split:
If the zygote splits very early (in the first 2 days after fertilization) they may develop separate placentas (chorion) and separate sacs (amnion). ... Most of the time in identical twins the zygote will split after 2 days, resulting in a shared placenta, but two separate sacs. ... Finally, the zygote may split extremely late, resulting in conjoined twins.
What I'm looking for is more specificity. At what time in the pregnancy does a split zygote result in twins who share a placenta and not a sac? What about conjoined twins (I'm most interested in the most common types of conjoined twins)?