How to organize a matrix with multiple variables into similar groups

Hi, I feel like this should be a relatively easy task but I can't figure out how to do it. I'm not at home right now, but later I can upload my code where I attempt to do this and maybe someone can tell me where I'm messing up.

But anyways, what I want to do is rearrange a matrix that has severable variables so that any row that is similar in every variable gets grouped together.

For example, each column represents a parameter of interest and each row is a separate dataset:

if true
110,4,3000
12,32,3009
14,28,127
112,6,2996
1245,18,2
2,189,37
11,34,3015
150,9,15
10,32,3008
114,3,3002
152,11,16

if true
110,4,3000
112,6,2996
114,3,3002

if true
12,32,3009
11,34,3015
10,32,3008

if true
150,9,15
153,11,16

The large matrix at the top becomes rearranged as the three smaller matrixes at the bottom (apologies for the formatting, I don't really get how the "code" tab on this forum works). Note that the result is matrices that contain only values that are close to each other for each variable (Each variable has its own known threshold that determines whether they are close enough). Rows from the original matrix that are not closely related to any other rows are discarded.