How to use ‘awk’ to determine the maximal value in multiple subsets of data within a file

Good morning,

I am using awk and trying to determine the max value of multiple sets of data within a file. Let's say I have the data:

    1 2 3
  4 5 6 7 8
  9 8 7 6 5
    4 3 2
    1 2 3
  4 6 7 8 7
  7 8 7 6 5
    4 3 2

I would like the output to be:

9
8

As every four lines is a subset of data, and 9 is the max value of the first set, and 8 is the max value of the second. I'm piping the above data in the first code block to:

awk 'NR%4<4 || NR==4 {for(i=1;i<=NF;i++) if($i>maxval) maxval=$i;}; END { print maxval;}' > file

But it only returns the max value of the whole file:

9

I was wondering if it is possible to print a max value of every n lines (n=4 here) in one awk command, or do I need to break it up? I had thought the NR%4<4 || NR==4 would tell the rest of the function to execute on every four lines, but seems like it's looking at all the data and only determining one 'maxval'.

Thanks.