Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
504 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. D3×#4004 | C2 | semidirect |
| 3. #11751804 | C2 | semidirect |
| 4. #11746802 | C2 | semidirect |
| 5. C3×#64931 | C2 | semidirect |
| 6. #11746508 | C2 | semidirect |
| 7. #11746508 | C2 | semidirect |
| 33. #64931 | D3 | semidirect |
| 370. C3×C5 | #1551 | semidirect |
| 435. C5 | #68485 | semidirect |
| 456. C3 | #10605005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11755164 | 2 |
| D3×#4004 | 2 |
| #11751804 | 2 |
| #11746802 | 2 |
| C3×#64931 | 2 |
| #11746508 | 2 |
| #10605005 | 3 |
| #68485 | 5 |