Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
294 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 14. #16840603 | C4 | semidirect |
| 15. C8×#92420 | C4 | semidirect |
| 19. #16839484 | C4 | semidirect |
| 20. #16839484 | C4 | semidirect |
| 21. #16839483 | C4 | semidirect |
| 22. C61×#322 | C4 | semidirect |
| 137. #322 | #6923 | semidirect |
| 139. C61 | #8141 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461537 | 2 |
| #21461023 | 2 |
| #21460644 | 2 |
| #21460642 | 2 |
| #21444110 | 2 |
| #8141 | 61 |