I've read two articles on DCNH subtypes from wikionics* and here is what I can recall:

They wanted to explain why certain types of the same socionic type exhibit different behaviour along the extroversion and introversion scale. From closer observation the same socionic type found in two people (or more) would manifest differently in terms of their first and secondary function.

Example: two people of the same type ISFP would not entirely act the same. One person acts extroverted and another acts introverted (hmm...how interesting they thought). They deduced the concept of extroveted-introvert to account for these differences of the same type.

The concept applies as needed to all introverts who demonstrate extroveted behaviour. Inversely, they realised the same phenomena with extroverts and so deduced the concept of introverted-extroverts. Hence the need for subtypes in addition to socionic typology. I think most of us can mostly agree to this - adimittedly it is a fiction in terms of what type made them realize there is subtypes and to further pursue investigating to other types.

From memory,

the dominant types are: ESFJ , ESTJ , ENTJ , ENFJ , ISFP , ISTP , INFP , INTP .

the normalizing types are: INTJ , INFJ , ISFJ , ISTJ , ENTP , ENFP , ESTP , ESFP .

Dominant and normalizing are compatible with each other in terms of their way of life and intimate relationships. Honestly not sure what that means yet for socionics as understood on socionics.com. I mean intimate relationships seems to include marriage I would assume. To prioritize amongst these two groups obviously duality would be most favourable but I'm unsure if that remains true when introducing the all other groups.

the creative types are: INTJ , INFJ , ISFJ , ISTJ , ENTP , ENFP , ESTP , ESFP .

the harmonizing types are: ESFJ , ESTJ , ENTJ , ENFJ , ISFP , ISTP , INFP , INTP .

Creative and harmonizing are compatible with each other, so on, ecctera. Like I was mentioning before, I'm not sure if an ESFJ is more compatibile with a INTJ or a ENTP ? Socionics would say INTJ and ESFJ are compatible but DCNH would say ESFJ and ENTP are more compatible - that is my interpretation.

The article mentions supervision, beneficial and activiation relationships. Familiar terms used in an unfamiliar way.

Dominants activate creatives, creatives activate normalizing, normalizing activates harmonizers, and harmonizers activates dominants.

Dominants supervise creatives, creatives supervise normalizing, normalizing supervises harmonizers, and harmonizers supervise dominants.

Dominants benefit creatives, creatives benefit normalizing, normalizing benefits harmonizers, and harmonizers benefit dominants.

Try compare that to your understanding of socionic interrelationships. I'm too exhausted and confused as to what it really means for socionics. This is only what I remember, the article gives a brief description of each type and there is more diagrams and relationships mentioned.

Some people argue if there is such a thing as subtypes and if so, is that a more ideal duality? - according to DCNH yes. However that complicates the socionics.com description of duality alot more than expanding upon it. If DCNH is true then socionics may have some revisions to consider.

As far as relevancy of enneagram system, at first it appears very general and contrived but then you discover there is wings and instinctual types which accounts for some differences in behaviour of the same type but then there is tri-types, ie. 5-2-9. Unbelievably, some people on the internet have gone through the bother of describing all the different combinations for a 5 tri-type.

Carl Jung is like the Charles Dawin for psychological types but dame this got way more confusing than evolution (Enneagram is influenced by Carl Jung's typology as is socionics).