Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
996 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 163 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. #21460219 | C2 | semidirect |
| 2. #21456737 | C2 | semidirect |
| 3. #21444905 | C2 | semidirect |
| 4. #21444484 | C2 | semidirect |
| 5. #21444237 | C2 | semidirect |
| 6. C61×#3138 | C2 | semidirect |
| 10. #16840415 | C22 | semidirect |
| 19. #16839508 | C22 | semidirect |
| 20. #16839491 | C22 | semidirect |
| 150. #3138 | D61 | semidirect |
| 179. C61 | #18727 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21460219 | 2 |
| #21456737 | 2 |
| #21444905 | 2 |
| #21444484 | 2 |
| #21444237 | 2 |
| C61×#3138 | 2 |
| #18727 | 61 |