Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
396 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21447440 | C2 | semidirect |
| 2. #21445865 | C2 | semidirect |
| 3. #21443804 | C2 | semidirect |
| 9. #16839544 | C22 | semidirect |
| 10. #16839519 | C22 | semidirect |
| 11. C22×D8×C61 | C4 | semidirect |
| 14. C61×#469 | C4 | semidirect |
| 18. C61×#427 | C4 | semidirect |
| 155. C22×D8 | Dic61 | semidirect |
| 159. #469 | Dic61 | semidirect |
| 164. #427 | Dic61 | semidirect |
| 170. C61 | #11868 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447440 | 2 |
| #21445865 | 2 |
| #21443804 | 2 |
| C61×#3058 | 2 |
| #11868 | 61 |