First Great Western I believe is owned by First Greater Western Ltd, which in turn is a part of First Group.
Interestingly, as I searched Companies House I noticed First also own the company name "First Greater Anglia Limited"; perhaps they will be bidding on the next Greater Anglia franchise?
First Greater Western Ltd are owned by First Rail Holdings Ltd, which is a wholly owned subsidiary of FirstGroup plc.
First Rail Holdings Ltd wholly own:
FIRST CAPITAL CONNECT LIMITED
FIRST CROSS COUNTRY LIMITED
FIRST DOCKLANDS LIMITED
FIRST EAST MIDLANDS LIMITED
FIRST GREAT NORTHERN LIMITED
FIRST GREATER ANGLIA LIMITED
FIRST GREATER WESTERN LIMITED
FIRST METRO LIMITED
FIRST SCOTRAIL LIMITED
FIRST SOUTH WESTERN LIMITED
FIRST WEST COAST LIMITED
(Apologies for the caps, I copied and pasted this)
FirstGroup plc also own a number of other rail related companies:
THE NEW GREAT EASTERN RAILWAY COMPANY LIMITED
GB▸ RAILWAYS GROUP PLC (and subsidiaries)
GREAT WESTERN HOLDINGS LIMITED (and subsidiaries)
HULL TRAINS COMPANY LIMITED (80%*)
FIRST/KEOLIS TRANSPENNINE LIMITED (55%*)
* = Shareholding according to the information this service holds, which isn't always correct or up-to-date