Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1078 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1078 conjugacy classes of subgroups — too many to draw. Only its 171 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. #21456814 | C2 | semidirect |
| 2. #21456264 | C2 | semidirect |
| 3. #21445125 | C2 | semidirect |
| 4. #21445108 | C2 | semidirect |
| 5. #21444454 | C2 | semidirect |
| 6. #21444430 | C2 | semidirect |
| 7. C61×#3549 | C2 | semidirect |
| 9. #16840312 | C22 | semidirect |
| 10. #16840157 | C22 | semidirect |
| 12. #16840152 | C22 | semidirect |
| 13. #16840152 | C22 | semidirect |
| 15. #16840121 | C22 | semidirect |
| 19. #16839819 | C22 | semidirect |
| 20. C2×#14519688 | C22 | semidirect |
| 21. #16839502 | C22 | semidirect |
| 22. #16839502 | C22 | semidirect |
| 185. #3549 | D61 | semidirect |
| 222. C61 | #19052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456814 | 2 |
| #21456264 | 2 |
| #21445125 | 2 |
| #21445108 | 2 |
| #21444454 | 2 |
| #21444430 | 2 |
| C61×#3549 | 2 |
| #19052 | 61 |