Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
412 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 76 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. C3×#66033 | C2 | semidirect |
| 2. C5×#5067 | C2 | semidirect |
| 4. #11746905 | C2 | semidirect |
| 5. #11746364 | C2 | semidirect |
| 6. #11745849 | C2 | semidirect |
| 7. #11745846 | C2 | semidirect |
| 29. #66033 | D3 | semidirect |
| 67. #5067 | D5 | semidirect |
| 322. C3×C5 | #1657 | semidirect |
| 369. C5 | #71955 | semidirect |
| 385. C3 | #10602042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66033 | 2 |
| C5×#5067 | 2 |
| #11747042 | 2 |
| #11746905 | 2 |
| #11746364 | 2 |
| #11745849 | 2 |
| #11745846 | 2 |
| #10602042 | 3 |
| #71955 | 5 |