diff --git a/scanpy/readwrite.py b/scanpy/readwrite.py
index f2aef41297..5ff556ddc5 100644
--- a/scanpy/readwrite.py
+++ b/scanpy/readwrite.py
@@ -219,7 +219,7 @@ def _read_legacy_10x_h5(filename, *, genome=None, start=None):
                 )
 
             dsets = {}
-            _collect_datasets(dsets, f)
+            _collect_datasets(dsets, f[genome])
 
             # AnnData works with csr matrices
             # 10x stores the transposed data, so we do the transposition right away
diff --git a/scanpy/tests/_data/10x_data/1.2.0/multiple_genomes.h5 b/scanpy/tests/_data/10x_data/1.2.0/multiple_genomes.h5
new file mode 100644
index 0000000000..3d04d4e909
Binary files /dev/null and b/scanpy/tests/_data/10x_data/1.2.0/multiple_genomes.h5 differ
diff --git a/scanpy/tests/test_read_10x.py b/scanpy/tests/test_read_10x.py
index e9cf188a4b..0f4373334a 100644
--- a/scanpy/tests/test_read_10x.py
+++ b/scanpy/tests/test_read_10x.py
@@ -73,6 +73,23 @@ def test_read_10x_h5_v1():
     assert_anndata_equal(spec_genome_v1, nospec_genome_v1)
 
 
+def test_read_10x_h5_v2_multiple_genomes():
+    genome1_v1 = sc.read_10x_h5(
+        ROOT / '1.2.0' / 'multiple_genomes.h5',
+        genome='hg19_chr21',
+    )
+    genome2_v1 = sc.read_10x_h5(
+        ROOT / '1.2.0' / 'multiple_genomes.h5',
+        genome='another_genome',
+    )
+    # the test data are such that X is the same shape for both "genomes",
+    # but the values are different
+    assert (genome1_v1.X != genome2_v1.X).sum() > 0, (
+        'loading data from two different genomes in 10x v2 format. '
+        'should be different, but is the same. '
+    )
+
+
 def test_read_10x_h5():
     spec_genome_v3 = sc.read_10x_h5(
         ROOT / '3.0.0' / 'filtered_feature_bc_matrix.h5',