diff --git a/test/Issue79Pkg/Project.toml b/test/Issue79Pkg/Project.toml
new file mode 100644
index 00000000..dc99e6b3
--- /dev/null
+++ b/test/Issue79Pkg/Project.toml
@@ -0,0 +1,10 @@
+name = "Issue79Pkg"
+uuid = "fa155e15-ec49-4eec-b540-f513de9043b2"
+authors = ["ExplicitImports tests"]
+version = "0.1.0"
+
+[weakdeps]
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+
+[extensions]
+LinearAlgebraExt = "LinearAlgebra"
diff --git a/test/Issue79Pkg/ext/LinearAlgebraExt.jl b/test/Issue79Pkg/ext/LinearAlgebraExt.jl
new file mode 100644
index 00000000..52bcaaa1
--- /dev/null
+++ b/test/Issue79Pkg/ext/LinearAlgebraExt.jl
@@ -0,0 +1,6 @@
+module LinearAlgebraExt
+
+include("SubmoduleExt.jl")
+using .SubmoduleExt
+
+end # module LinearAlgebraExt
diff --git a/test/Issue79Pkg/ext/SubmoduleExt.jl b/test/Issue79Pkg/ext/SubmoduleExt.jl
new file mode 100644
index 00000000..bf9af91f
--- /dev/null
+++ b/test/Issue79Pkg/ext/SubmoduleExt.jl
@@ -0,0 +1,7 @@
+module SubmoduleExt
+
+export LOCAL_CONST
+
+const LOCAL_CONST = 1
+
+end # module SubmoduleExt
diff --git a/test/Issue79Pkg/src/Issue79Pkg.jl b/test/Issue79Pkg/src/Issue79Pkg.jl
new file mode 100644
index 00000000..e291d3d8
--- /dev/null
+++ b/test/Issue79Pkg/src/Issue79Pkg.jl
@@ -0,0 +1,3 @@
+module Issue79Pkg
+
+end # module Issue79Pkg
diff --git a/test/issue_79_test.jl b/test/issue_79_test.jl
new file mode 100644
index 00000000..11c70bbd
--- /dev/null
+++ b/test/issue_79_test.jl
@@ -0,0 +1,10 @@
+using Issue79Pkg
+using LinearAlgebra
+
+ext_mod = Base.get_extension(Issue79Pkg, :LinearAlgebraExt)
+
+@testset "extension submodule analyzable (#79)" begin
+    @test ext_mod !== nothing
+    @test isdefined(ext_mod, :SubmoduleExt)
+    @test check_no_implicit_imports(Issue79Pkg) === nothing
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index 5d1a14d1..d4735855 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,5 +1,6 @@
 using Pkg
 Pkg.develop(; path=joinpath(@__DIR__, "TestPkg"))
+Pkg.develop(; path=joinpath(@__DIR__, "Issue79Pkg"))
 Pkg.precompile()
 using ExplicitImports
 using ExplicitImports: analyze_all_names, has_ancestor, should_skip,
@@ -105,6 +106,10 @@ include("issue_140.jl")
                                 (; name=:groupby, source=DataFrames.DataAPI)]
     end
 
+    @testset "Extension submodules (#79)" begin
+        include("issue_79_test.jl")
+    end
+
     @testset "Field names shadowing external globals (#111)" begin
         include("issue_111_test.jl")
     end