Create a grid in OpenGL

I need to generate a NxN resolution grid in the xy-plane with OpenGL. The final grid needs to be made by triangles (GL_TRIANGLES), so it should seem like the following example:

 ^
 *   |  ----------
 *   |  |\ |\ |\ |
 *   |  | \| \| \|
 *   |  ----------
 *   |  |\ |\ |\ |
 * y |  | \| \| \|
 *   |  ----------
 *   |  |\ |\ |\ |
 *   |  | \| \| \|
 *   |  ----------
 *   |
 *   |-------------->
 *          x

Note that I need to store the grid in vertex-index form (given the structures by parameters).

My code at this point:

void generate_grid(
std::uint32_t N,
std::vector<glm::vec3>* vertices,
std::vector<glm::uvec3>* indices)
{
for (int i = 0; i < N; i++) {
    glBegin(GL_TRIANGLES);
for (int j = 0; j < N; j++) {
    int vertexNum = indices;  // Index for vertex j of face i.
    double[] vertexCoords = vertices[vertexNum];  // The vertex itself.
    glVertex3f(vertexCoords, 0);
}

glEnd();

} 

Any advice? Regards.