"Formula One Group" strictly refers to Formula One Management, Formula One Administration and Formula One Licensing BV, which are subsidiaries of the Formula One Holdings holding company. However Delta Topco owns other Formula One businesses which are referred to in the same way.
In 1995 the FIA decided to grant the commercial rights to F1 to Formula One Administration (managed by FOM) for a 14 year period. In exchange, Ecclestone would provide an annual payment. With FOM having exclusive rights to popular team names like Team McLaren, WilliamsF1, and Tyrrell Formula One, the aforementioned teams protested by rejecting the following Concorde Agreement in 1997. Team McLaren, WilliamsF1, Scuderia Ferrari and Renault F1 formed GPWC Holdings and threatened to form a rival racing franchise in 2008 when their contracts ended in 2007.
EM.TV's acquisitions caused it financial difficulties; following its announcement that its 2000 earnings would be below expectations and it was struggling with its debts, the share price dropped 90%. In February the Kirch Group agreed to rescue EM.TV in return for a stake in the company and control of Speed Investments. The two companies also agreed to exercise EM.TV's option to purchase another 25% of SLEC for approximately £600 million in late-March 2001. To raise Speed Investments' share of SLEC to 75% Kirch borrowed €1.6 billion, €1 billion from Bayerische Landesbank and the rest from Lehman Brothers and JPMorgan Chase. Kirch's involvement raised concerns among the major motor manufacturers who participate in Formula One; BMW, DaimlerChrysler, Fiat, Ford, and Renault formed GPWC Holding BV to secure better representation of the manufacturers in F1, improved financial conditions for the teams, stability for the championship, and maintenance of free-to-air television coverage.
Due to the agreement associated with their shareholding SLEC was controlled by Kirch, who hence controlled the board of Formula One Holdings (FOH). Due to huge losses and massive expenditure, Kirch's creditors put the company into receivership in 2002. These banks dismantled the group. Kirch's share of SLEC was retained by Bayerische Landesbank, JPMorgan Chase and Lehman Brothers (through Speed Investments).
Before they could exercise their rights as shareholders they had to seek clearance from the European Commission. In the intervening period Ecclestone instituted changes in the boards of SLEC, FOH, Formula One Administration (FOA) and Formula One Management (FOM) which in effect put Bambino Holdings in control of those companies.
In mid-November 2004, the three banks sued Ecclestone for more control over the sport, prompting speculation that Ecclestone might altogether lose the control he has maintained for more than thirty years. A two-day hearing began on November 23, but after the proceedings had ended the following day, Justice Andrew Park announced his intention to reserve ruling for several weeks. On December 6, 2004, Park read his verdict, stating that "In [his] judgment it is clear that Speed's contentions are correct and [he] should therefore make the declarations which it requests"
However, Ecclestone insisted that the verdict - seen almost universally as a legal blow to his control of Formula One - would mean "nothing at all"
He stated his intention to appeal the decision.
The following day, at a meeting of team bosses at Heathrow Airport in London, Ecclestone offered the teams a total of £260,000,000 over three years in return for unanimous renewal of the Concorde Agreement, which expires in 2008
Weeks later, Gerhard Gibkowsky, a board member of Bayerische Landesbank and the chairman of SLEC, stated that the banks had no intention to remove Ecclestone from his position of control

On March 30 2006 CVC purchased the 14.1% share of SLEC held by Lehman Brothers to give Alpha Prema full control of the Formula One Group.
In its annual accounts filed with Companies House, FOA reported turnover of $750 million and pre-tax profits of $447 million (up from $215m in 2003 and $127m in 2002). This has allowed the company to slash its debts by $347 million to $121 million. 
The president of FOM is Bernie Ecclestone who has presided over the company since it has existed in its current form.
These rights were originally granted to the Formula One Constructors Association (FOCA) by the FIA under the terms of the Concorde Agreement. FOCA allowed FOPA to manage the rights on its behalf.
In 1995 the FIA decided to transfer Formula One's commercial rights from FOCA to Formula One Administration for a 14 year period. In exchange, Ecclestone would provide an annual payment. Team McLaren, WilliamsF1 and Tyrrell, protested by rejecting the proposed Concorde Agreement (negotiations for which started as early as 1993). Ken Tyrrell in particular was enraged by the fact that Ecclestone, as President of FOCA had negotiated the transfer of the rights from the organisation to his own company.
FOPA ceased to exist in 1997 with the reorganisation of Eccelstone's companies which are now headed by SLEC.
Allsport Management was founded by Paddy McNally who had begun to work with Bernie Ecclestone in the late 1970s. McNally, who was a former Marlboro sponsorship consultant, came up with a solution to "tidy up" trackside advertising; This solution was called "themed advertising" where one advertiser is given total exposure at one part of the track. This is in contrast to the Monaco Grand Prix, the only grand prix where Allsport is not involved, where space is sold such that multiple advertisers are visible in every picture. This is arguably less effective.
In 2006 Allsport Management (and the related Allsopp Parker & Marsh companies) were acquired by the Formula One Group. This deal, estimated to be worth $350m, simplified the formerly secretive structure of Formula One and means all the revenues from the sport are now paid directly into the Formula One Group.