Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
470 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 470 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 |
|---|---|---|
| 2. #21445619 | C2 | semidirect |
| 3. #21443942 | C2 | semidirect |
| 4. #21443940 | C2 | semidirect |
| 9. #16839552 | C4 | semidirect |
| 10. #16839549 | C4 | semidirect |
| 13. C23×C8×C61 | C4 | semidirect |
| 17. C61×#424 | C4 | semidirect |
| 19. C61×#407 | C4 | semidirect |
| 20. C61×#405 | C4 | semidirect |
| 155. C23×C8 | Dic61 | semidirect |
| 159. #424 | Dic61 | semidirect |
| 163. #407 | Dic61 | semidirect |
| 165. #405 | Dic61 | semidirect |
| 169. C61 | #12623 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447460 | 2 |
| #21445619 | 2 |
| #21443942 | 2 |
| #21443940 | 2 |
| C61×#2929 | 2 |
| #12623 | 61 |