Conversations are sorted in a reverse chronological order based on their Start Time, with unpublished Conversations appearing first.
For example, if you have created two Conversations that start on January 22nd and January 23rd, the Conversation starting on January 23rd will be sorted first, then the January 22nd Conversation. If you have a Conversation that has no start date/time, that Conversation will appear before the ones on January 23rd and 22nd.