Glasgow chief executive David Jordan said: 'It is an enormously hard draw but as second seeds from Scotland we expected that.
"Toulouse and Northampton are recent champions, while Llanelli have been the most consistent Welsh performers in the competition since it began. The prospect of hosting Toulouse at Hughenden is certainly mouth-watering and we are looking forward to the challenge."
The exact dates and times of the matches will be released approximately in mid August (2 months before the tournament kicks-off). The reason for the times and dates of the fixtures being released in mid August is because ERC will be consulting with its broadcaster partners to decide the televised fixtures.
POOL 1: London Wasps, Calvisano, Biarritz Olympique, Leicester Tigers.
POOL 2: Benetton Treviso, Leinster, Bath Rugby, Bourgoin.
POOL 3: Llanelli Scarlets, Glasgow Warriors, Northampton Saints, Toulouse.
POOL 4: Munster, Neath-Swansea Ospreys, Castres Olympique, NEC Harlequins.
POOL 5: Edinburgh, Perpignan, Newport Gwent Dragons, Newcastle Falcons.
POOL 6: Stade Français Paris, Ulster, Cardiff Blues, Gloucester.
ROUND 1
22/23/24 October 2004
Glasgow Warriors v Northampton Saints
ROUND 2
29/30/31 October 2004
Stade Toulousain v Glasgow Warriors
ROUND 3
3/4/5 December 2004
Glasgow Warriors v Llanelli Scarlets
ROUND 4
10/11/12 December 2004
Llanelli Scarlets v Glasgow Warriors
ROUND 5
7/8/9 January 2005
Glasgow Warriors v Stade Toulousain
ROUND 6
14/15/16 January 2005
Northampton Saints v Glasgow Warriors