Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
536 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 131 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. #21454723 | C2 | semidirect |
| 2. #21448031 | C2 | semidirect |
| 3. #21447992 | C2 | semidirect |
| 4. #21447892 | C2 | semidirect |
| 5. #21447764 | C2 | semidirect |
| 6. #21447715 | C2 | semidirect |
| 7. #21447635 | C2 | semidirect |
| 8. C61×#3176 | C2 | semidirect |
| 18. #16839584 | C22 | semidirect |
| 19. #16839583 | C22 | semidirect |
| 20. #16839575 | C22 | semidirect |
| 23. #16839540 | C22 | semidirect |
| 25. C61×#499 | C22 | semidirect |
| 26. C61×#493 | C22 | semidirect |
| 30. C61×#442 | C22 | semidirect |
| 162. #3176 | D61 | semidirect |
| 179. #499 | C2×D61 | semidirect |
| 180. #493 | C2×D61 | semidirect |
| 188. #442 | C2×D61 | semidirect |
| 199. C61 | #33692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454723 | 2 |
| #21448031 | 2 |
| #21447992 | 2 |
| #21447892 | 2 |
| #21447764 | 2 |
| #21447715 | 2 |
| #21447635 | 2 |
| C61×#3176 | 2 |
| #33692 | 61 |