Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
364 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 1. #11751184 | C2 | semidirect |
| 2. C5×#5088 | C2 | semidirect |
| 4. #11746994 | C2 | semidirect |
| 5. C3×#64767 | C2 | semidirect |
| 6. #11745869 | C2 | semidirect |
| 7. #11745853 | C2 | semidirect |
| 29. #64767 | D3 | semidirect |
| 51. #5088 | D5 | semidirect |
| 270. C3×C5 | #1681 | semidirect |
| 318. C5 | #68446 | semidirect |
| 333. C3 | #10601994 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751184 | 2 |
| C5×#5088 | 2 |
| #11747045 | 2 |
| #11746994 | 2 |
| C3×#64767 | 2 |
| #11745869 | 2 |
| #11745853 | 2 |
| #10601994 | 3 |
| #68446 | 5 |