The Alphabet Chromosome

Vim (no external tools), 106 bytes

Newlines for clarity:

:h<_↵↵↵YZZPllabc♥
:s/./\u&&/g↵
qa6li↵♥q7@a3i ♥fY
i↵    →→↵  →↵→ð♥
ʌHA ♥9l
qbmaʌ99jY$P`ah@bq@b
y11G:g//m0↵P

Here ↵ is Return, → is Right, ♥ is Escape, ʌ is CTRL-V, and ð is Delete.

PowerShell v2+, 175 169 163 154 bytes

($x=(-join(65..67+66..86|%{$_;32+$_}|%{[char]$_})-split'(.{6})'-ne'')+'   WwXx'+'       Yy'+(' '*9+'Z')|% *ht 10|%{$_+-join$_[9..0]})
' '*9+'zz'
$x[10..0]

Try it online!

Abuses the fact that default Write-Output at the end of execution inserts a newline between elements.

The first line constructs the branches. We loop over two ranges corresponding to the ASCII values for the capital letters, each iteration output a char array of that letter and that letter +32 (which is the lowercase ASCII point). That's -joined together into one long string, then -split on every six elements (encapsulated in parens so they're preserved), followed by a -ne'' to pull out the empty elements as a result of the split, thus forming an array of strings.

These strings in an array get array-concatenation to add on the WwXx, Yy, and Z elements, then a PadRight 10 to make them all the appropriate width. At this point we have an array of strings like the following (one element per line).

AaBbCc    
BbCcDd    
EeFfGg    
HhIiJj    
KkLlMm    
NnOoPp    
QqRrSs    
TtUuVv    
   WwXx   
       Yy 
         Z

That whole array is piped to another loop to construct the mirrored strings with -join and array-reversing [9..0].

AaBbCc        cCbBaA
BbCcDd        dDcCbB
EeFfGg        gGfFeE
HhIiJj        jJiIhH
KkLlMm        mMlLkK
NnOoPp        pPoOnN
QqRrSs        sSrRqQ
TtUuVv        vVuUtT
   WwXx      xXwW   
       Yy  yY       
         ZZ         

We save the resulting strings into $x and enclose in parens to also place a copy on the pipeline.

The next line places the zz string on the pipeline, then the $x array in reverse order. All of those are left on the pipeline and output is implicit.

PS C:\Tools\Scripts\golfing> .\alphabet-chromosome.ps1
AaBbCc        cCbBaA
BbCcDd        dDcCbB
EeFfGg        gGfFeE
HhIiJj        jJiIhH
KkLlMm        mMlLkK
NnOoPp        pPoOnN
QqRrSs        sSrRqQ
TtUuVv        vVuUtT
   WwXx      xXwW   
       Yy  yY       
         ZZ
         zz
         ZZ
       Yy  yY       
   WwXx      xXwW   
TtUuVv        vVuUtT
QqRrSs        sSrRqQ
NnOoPp        pPoOnN
KkLlMm        mMlLkK
HhIiJj        jJiIhH
EeFfGg        gGfFeE
BbCcDd        dDcCbB
AaBbCc        cCbBaA

-9 bytes thanks to mazzy.

Python 2, 230 bytes

s='';m=['AaBbCc','BbCcDd','EeFfGg','HhIiJj','KkLlMm','NnOoPp','QqRrSs','TtUuVv','   WwXx',' '*7+'Yy',' '*9+'Z'];
p=lambda l:l.ljust(10)+l[::-1].rjust(10)+'\n';
for l in m:s+=p(l);
s+=' '*9+'zz\n';
for l in m[::-1]:s+=p(l)
print s