Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
512 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 108 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. #11747000 | C2 | semidirect |
| 3. #11746859 | C2 | semidirect |
| 4. C5×#4547 | C2 | semidirect |
| 5. C3×#64767 | C2 | semidirect |
| 6. #11745854 | C2 | semidirect |
| 7. #11745854 | C2 | semidirect |
| 31. #64767 | D3 | semidirect |
| 62. #4547 | D5 | semidirect |
| 314. C3×C5 | #1540 | semidirect |
| 368. C5 | #68417 | semidirect |
| 385. C3 | #10599210 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756484 | 2 |
| #11747000 | 2 |
| #11746859 | 2 |
| C5×#4547 | 2 |
| C3×#64767 | 2 |
| #11745854 | 2 |
| #10599210 | 3 |
| #68417 | 5 |