Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
564 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 564 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. #21454730 | C2 | semidirect |
| 2. #21448031 | C2 | semidirect |
| 3. #21447987 | C2 | semidirect |
| 4. #21447892 | C2 | semidirect |
| 5. #21447764 | C2 | semidirect |
| 6. #21447715 | C2 | semidirect |
| 7. #21447631 | C2 | semidirect |
| 8. C61×#3184 | C2 | semidirect |
| 18. #16839584 | C22 | semidirect |
| 19. #16839583 | C22 | semidirect |
| 20. #16839575 | C22 | semidirect |
| 23. #16839540 | C22 | semidirect |
| 25. C61×#498 | C22 | semidirect |
| 26. C61×#493 | C22 | semidirect |
| 31. C61×#442 | C22 | semidirect |
| 107. Dic244 | #41 | semidirect |
| 109. D488 | #41 | semidirect |
| 165. #3184 | D61 | semidirect |
| 182. #498 | C2×D61 | semidirect |
| 183. #493 | C2×D61 | semidirect |
| 192. #442 | C2×D61 | semidirect |
| 202. C61 | #33688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454730 | 2 |
| #21448031 | 2 |
| #21447987 | 2 |
| #21447892 | 2 |
| #21447764 | 2 |
| #21447715 | 2 |
| #21447631 | 2 |
| C61×#3184 | 2 |
| #33688 | 61 |