In order to find the volume group that a filesystem is on:
df -g <file system>
Filesystem GB blocks Free %Used Iused %Iused Mounted on
/dev/<filesystemname> 40.00 2.42 94% 541 1% /oracle/EXD
lslv <filesystem name>
VOLUME GROUP: cstdexdvg VG IDENTIFIER: 00c724b200004c000000011f1381fa92
VG STATE: active PP SIZE: 128 megabyte(s)
VG PERMISSION: read/write TOTAL PPs: 959 (122752 megabytes)
MAX LVs: 256 FREE PPs: 366 (46848 megabytes)
LVs: 6 USED PPs: 593 (75904 megabytes)
OPEN LVs: 6 QUORUM: 2 (Enabled)
TOTAL PVs: 1 VG DESCRIPTORS: 2
STALE PVs: 0 STALE PPs: 0
ACTIVE PVs: 1 AUTO ON: yes
MAX PPs per VG: 32512
MAX PPs per PV: 1016 MAX PVs: 32
LTG size (Dynamic): 256 kilobyte(s) AUTO SYNC: no
HOT SPARE: no BB POLICY: relocatable