How to Generate a Matrix of Specific Row-Column Combinations (to list certain permutations) Without Using Loops

I want to create a matrix of specific row-column combinations. The rows should be considered pair-wise, and the columns should be the three columns that follow. So, this is like a setup for me to compare each pair of rows with all the pairs of rows in the three columns that follow. I do not want to use a loop, because my matrix is very large.

For example, let’s say that I have a matrix:

[a b c d;
e f g h;
i j k l;
m n o p]

So, the final matrix will look like this (hyphens for clarity): // Note that the first element after each hyphen/brace corresponds to the element in the row-pair being considered, while the three elements that follow belong to the three columns that follow. This means that the pair of elements in the row-pairs being considered are replicated in the final matrix.

[a b c d – b c d NaN – c d NaN NaN – d NaN NaN NaN; 
// NaN’s because there aren’t column numbers 5:7 in the original matrix. 
// The matrix I have will be very large (with 10000s of rows and columns) and so will actually need NaN's only towards the very last columns.
e f g h – f g h NaN – g h NaN NaN – h NaN NaN NaN;
a j k l – b k l NaN – c l NaN NaN – d NaN NaN NaN;
e n o p – f o p NaN – g p NaN NaN – h NaN NaN NaN;
i b c d – j c d NaN – k d NaN NaN – l NaN NaN NaN;
m f g h – n o p NaN – o h NaN NaN – p NaN NaN NaN;
i j k l – j k l NaN – k l NaN NaN – l NaN NaN NaN;
m n o p – n o p NaN – o p NaN NaN – p NaN NaN NaN]

Does anyone have ideas on how to get this done? I tried using repelem and repmat, but I cannot think of a way to get rows pairwise (in the way that one can get odd rows using (1:2:end, :), for example). Thank you for your time!

[Image Analyst]

Can you also give an example with actual numbers and no dashes or comments? I don't know what "compare" means to you (e.g. subtraction) and don't know if all "-" are hyphens or minus signs.