Losing page number on form post laravel - php

Question

I have two dropdowns one for asc desc and one with the field name. When I change page I am able to keep the order and order_by parameter and the page number. When I change one of the dropdown a postback happens In that case I lose the page number. How can I fix this problem.
Here is the url I want
home?orderby=created_at&order=desc&page=2
Here is the url I have in the case of a dropdown change
home?orderby=created_at&order=desc
Here is my front end code
<form action="{{ route('home') }}" method="GET">
<div class="row">
<div class="col-2">
<label for="nom">Trier par :</label>
</div>
<div class="col-tier form-group">
<select class="form-control" name="orderby" id="orderby" onchange="this.form.submit()">
<option value="nom" {{ Request()->orderby == 'nom' ? ' selected' : '' }}>Nom</option>
<option value="created_at" {{ Request()->orderby == 'created_at' ? ' selected' : '' }}>Date de création</option>
<option value="updated_at" {{ Request()->orderby == 'updated_at' ? ' selected' : '' }}>Date de modification</option>
</select>
</div>
<div class="col-tier form-group ">
<select class="form-control" name="order" id="order" onchange="this.form.submit()">
<option value="desc" {{ Request()->order == 'desc' ? ' selected' : '' }}>Desc</option>
<option value="asc" {{ Request()->order == 'asc' ? ' selected' : '' }}>Asc</option>
</select>
</div>
</div>
</form>
<div id="pagination" class="d-flex justify-content-center">
{{ $grilles->appends(request()->except('page'))->links() }}
</div>
Here is the code of the controlleur
public function index(Request $request)
{
$user = Auth::user();
$sort = "ASC";
if($request->get('order')==="desc")
{
$sort="DESC";
}
if ($request->get('orderby')==="created_at") {
$grilles = Grille::orderBy('created_at', $sort)->paginate(15)->appends(request()->query());
} else if ($request->get('orderby')==="updated_at") {
$grilles =Grille::orderBy('updated_at', $sort)->paginate(15)->appends(request()->query());
}
else{
$grilles =Grille::orderBy('nom', $sort)->paginate(15)->appends(request()->query());
}
return view('home', compact('grilles'));
}
<div id="pagination" class="d-flex justify-content-center">
{{ $grilles->appends(request()->except('page'))->links() }}
</div>