Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
820 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 820 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. #21446652 | C2 | semidirect |
| 2. #21444541 | C2 | semidirect |
| 3. #21444454 | C2 | semidirect |
| 4. #21444327 | C2 | semidirect |
| 6. #16839819 | C22 | semidirect |
| 7. #16839786 | C22 | semidirect |
| 9. #16839608 | C22 | semidirect |
| 16. C61×#555 | C4 | semidirect |
| 18. D42×C61 | C4 | semidirect |
| 162. #555 | Dic61 | semidirect |
| 164. D42 | Dic61 | semidirect |
| 177. C61 | #8491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21446652 | 2 |
| #21444541 | 2 |
| #21444454 | 2 |
| #21444327 | 2 |
| C61×#3549 | 2 |
| #8491 | 61 |