Angular 2 - Child routes load parent component

Angular is a SPA(Single Page Application) platform, so it will have a technique for single paging. You need to include <router-outlet> into your PrivateComponent to let Angular loads child routes' components there. Router-outlet shows the place where child component will be loaded.

For more see Defining Child Routes

You will not need another <router-outlet> in the component.

Instead of defining a component in the parent route have a root path in children that points to the parent, like so:

{ path: 'admin', children: [
    { path: '', component: PrivateComponent },
    { path: 'account-settings', children: [
        { path: '', component: AccountSettingsComponent},
        { path: 'user-information', component: UserInformationComponent},
        { path: 'companys-information', component: CompanysInformationComponent}
    ] },
] },

On the other hand I can see the benefit of using an additional <router-outlet> if you want to display a common element for each child routes i.e. a header.