Another way would be to pass each line of data into a series of nested maps to split on whitespace then on the equals to produce an anonymous hash (hashref) which is passed to a third map. There the value of the "type" key is preserved, the "type" key/value pair deleteed from the hashref and finally the preserved key, with its value being the hashref, passed into %hash.

use strict;
use warnings;

use Data::Dumper;

open my $inFH, q{<}, \ <<EOF or die $!;
type=first a=1 b=2 c=3
type=second d=4 e=5 f=6
type=third g=7 h=8 i=9
EOF

my %hash =
   map {
       my $key = $_->{ type };
       delete $_->{ type };
       ( $key => $_ );
       }
   map { { map { split m{=} } split } }
   <$inFH>;

close$inFH or die $!;

print Data::Dumper
   ->new( [ \ %hash ], [ qw{ *hash } ] )
   ->Sortkeys( 1 )
   ->Dumpxs();
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The output.

%hash = (
          'first' => {
                       'a' => '1',
                       'b' => '2',
                       'c' => '3'
                     },
          'second' => {
                        'd' => '4',
                        'e' => '5',
                        'f' => '6'
                      },
          'third' => {
                       'g' => '7',
                       'h' => '8',
                       'i' => '9'
                     }
        );
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I hope this is helpful.

Update: Revised wording, s/a series of/nested/.