Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
694 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 694 conjugacy classes of subgroups — too many to draw. Only its 116 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. #21461947 | C2 | semidirect |
| 2. #21461947 | C2 | semidirect |
| 3. #21461740 | C2 | semidirect |
| 4. #21461015 | C2 | semidirect |
| 15. #16840139 | C4 | semidirect |
| 16. #16840138 | C4 | semidirect |
| 19. C61×#493 | C4 | semidirect |
| 75. D61⋊C8 | D8 | semidirect |
| 161. #493 | #6923 | semidirect |
| 170. C61 | #9832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461947 | 2 |
| #21461740 | 2 |
| #21461015 | 2 |
| #493×D61 | 2 |
| #9832 | 61 |