In Chapter XVI of " The Mediums' Book",  Allan Kardec presents a tabular view of the principal varieties of mediumship.  Regarding the entire set of divisions, he writes: 

We have grouped the different varieties of mediums according to similarity of causes and effects, but without offering this classification as in any way absolute.  Some of them are frequently met with; others, on the contrary are rare, and even exceptional, and we have been careful to mark them as such. The indications thus given have all been furnished by spirits, who moreover, have reviewed and carefully revised our list and completed it by various observations, so that it may be said to be entirely their work.  

Some of these are discussed in this site.  However, it should be pointed out here that Kardec does list additional divisions. We make reference to them below,  to point out that such varieties exist and have been classified, and we refer you to "The Medium's Book" for more information.

Please see Chapter XVI of "The Medium's Book" for the definitions of these varieties of mediums (Keep in mind that these varieties include those which involve communications provoked by inferior spirits):

According to the Development of the Medianimic Faculty:  Novice, Unproductive, Fully Formed, Laconic, Explicit, Experienced, Flexible, Exclusive, Those For Evocations, Those Who Receive Spontaneous Communications.

According to Kind and Specialty of Communications: Verse-making, Poetic, Positive, Literary, Incorrect, Historical, Scientific, Medical, Religious, Philosophic and Moralistic, Those For Trivial and Obscene Communications.

According to Physical Qualities of the Medium: Calm, Rapid, Convulsive.