Fetch array of 'data' from HTTPClient API call using Observables in Angular

I have a service from which I want to access data which are in this form from an HTTP GET request:

   "data": [
    {
        "id": "432",
        "Time": "06:25",
        "Place": "Atalanta"
    },
    {
        "id": "581",
        "Time": "18:21",
        "Place": "Georgia"
    }
   ]

I've created a service to call it which does this return method

return this.http.get<DataGroup>(url);

and two class models to access those data:

import { DataGroupValue } from './DataGroupValue';

export class DataGroup{
    value: DataGroupValue[] = [];
}

(don't know if it's doing the job right though)

export class DataGroupValue {
    id: string;
    Time: string;
    Place: string;
}

and a component that tries to call this method which doesn't work

export class TestPlannerComponent implements OnInit {

  DataGroupValues = new Array<DataGroup>();

  constructor(private dataService: DataService ) { }

  ngOnInit(): void {
    this.dataService.GetDataGroup.subscribe((res:DataGroup))=>{
        this.DataGroupValues=res; //errors here
      }
  }

}

How can we access those values?

Your types do not match at all, so Typescript corrently tells you that. If you are indeed receiving response as an object data that contains an array:

 {
   "data": [
    {
        "id": "432",
        "Time": "06:25",
        "Place": "Atalanta"
    },
    {
        "id": "581",
        "Time": "18:21",
        "Place": "Georgia"
    }
   ]
}

You need to create models that match these properties. I like to use interfaces:

export interface DataGroupResponse {
  data: DataGroupValue[]; // use 'data' as that is what you are getting!
}

export interface DataGroupValue {
  id: string;
  Time: string;
  Place: string;
}

Then you need to correctly tell http what you are receiving, so what you are receiving as response is of type DataGroupPayload. Here I would already extract the array from data and send back the array as DataGroupValue:

import { map } from 'rxjs/operators';

// ...

getDataGroup(): Observable<DataGroup[]> { // send back the array
  return this.http.get<DataGroupPayload>(url).pipe(  // what you are receiving is "DataGroupPayload"
    map((data: DataGroupPayload) => data.data as DataGroupValue[])
  )
}

Then in your component,

dataGroupValues = <DataGroupValue[]>[]; // array

ngOnInit(): void {
  this.dataService.getDataGroup().subscribe((res: DataGroupValue[]))=>{
     this.dataGroupValues = res;
  }
}

PS, notice I used camelCase, it's ususally how we name functions/variables.