$ split -d -l 6 bigfile subfile

will create subfile00 subfile01 .... with each file of 6 lines

As you want 3 files in output, the l value has to be caluculated like this:

$ awk 'END {printf("%d\n",NR/3+.5)}' bigfile

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** The above way of rounding may go wrong in some cases, e.g. suppose the file is having 17 lines, 

$ awk 'END {printf("%d\n",NR/5+.5)}' bigfile
3

then,

$ split -d -l 3 bigfile subfile

will create 4 subfiles, which is wrong. 
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I am sure there can be better solutions to this. Group please.