Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
512 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 135 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. #21456478 | C2 | semidirect |
| 2. #21448038 | C2 | semidirect |
| 3. #21447995 | C2 | semidirect |
| 4. #21447900 | C2 | semidirect |
| 6. #21447710 | C2 | semidirect |
| 7. #21447635 | C2 | semidirect |
| 11. #16840164 | C22 | semidirect |
| 12. #16840142 | C22 | semidirect |
| 16. #16839870 | C22 | semidirect |
| 18. #16839586 | C22 | semidirect |
| 19. #16839583 | C22 | semidirect |
| 20. #16839577 | C22 | semidirect |
| 23. #16839540 | C22 | semidirect |
| 193. C61 | #33693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456478 | 2 |
| #21448038 | 2 |
| #21447995 | 2 |
| #21447900 | 2 |
| #21447770 | 2 |
| #21447710 | 2 |
| #21447635 | 2 |
| C61×#2955 | 2 |
| #33693 | 61 |