Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
462 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 108 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. #21461613 | C2 | semidirect |
| 4. #21461033 | C2 | semidirect |
| 5. #21460715 | C2 | semidirect |
| 6. #21460709 | C2 | semidirect |
| 14. #16840621 | C4 | semidirect |
| 15. #16840620 | C4 | semidirect |
| 22. #16839841 | C4 | semidirect |
| 24. D4×#92418 | C4 | semidirect |
| 25. #16839827 | C4 | semidirect |
| 30. C61×#436 | C4 | semidirect |
| 212. #436 | #6923 | semidirect |
| 231. C61 | #8253 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461613 | 2 |
| #21461316 | 2 |
| #21461198 | 2 |
| #21461033 | 2 |
| #21460715 | 2 |
| #21460709 | 2 |
| #21454528 | 2 |
| #8253 | 61 |