How can I use Itertools::group_by without cloning or the error "cannot move out of a value which is behind a shared reference"?

Question

I have what seems to me like a simple Itertools::group_by task, but I can't make it compile unless I add clone calls.

use itertools::Itertools; // 0.9.0;
use std::collections::HashMap;

#[derive(Debug, Clone, PartialEq, Eq)]
pub struct Server {
    pub desc: String,
    pub group_name: Option<String>,
}

fn main() {
    let servers = vec![
        Server {
            desc: "one".to_string(),
            group_name: Some("A".to_string()),
        },
        Server {
            desc: "two".to_string(),
            group_name: Some("A".to_string()),
        },
        Server {
            desc: "three".to_string(),
            group_name: None,
        },
    ];

    let mut servers_by_group_name = HashMap::new();
    for (key, group) in &servers.into_iter().group_by(|s| s.group_name) {
        servers_by_group_name.insert(key, group.collect::<Vec<_>>());
    }
}

playground

The error is:

error[E0507]: cannot move out of `s.group_name` which is behind a shared reference
  --> src/main.rs:27:59
   |
27 |     for (key, group) in &servers.into_iter().group_by(|s| s.group_name) {
   |                                                           ^^^^^^^^^^^^
   |                                                           |
   |                                                           move occurs because `s.group_name` has type `std::option::Option<std::string::String>`, which does not implement the `Copy` trait
   |                                                           help: consider borrowing the `Option`'s content: `s.group_name.as_ref()`

The error is quite clear to me. I know I could make it go away by cloning the s.group_name in the group_by. I believe I could also use .iter() instead of .into_iter(), then it would possibly work, but then I would have a Vec<&Server> in the values of my map, but I'd really like a Vec<Server> (because my next step is wrapping that Server in a new datastructure and I really want the ownership).

Is there a way to implement this without cloning the group_name in the group_by closure?