In general terms, a group of companies is a parent company together with all its subsidiaries and appropriate proportionate interests in associated undertakings and joint ventures.
In practice the exact membership of the group may differ for financial reporting purposes and for tax purposes.
Financial reporting - accounting practices.
For financial reporting purposes, the membership of the financial reporting group is almost always mandatory/automatic.
The membership of tax groups may also differ in their details for different tax purposes.
For most UK tax purposes, companies which are eligible to be grouped may usually elect to be grouped for different tax purposes, but group tax treatment is not normally mandatory.
More broadly, similar relationships in respect of direction and control in any diversified organisation, regardless of the precise legal ownership structure.