Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
486 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 3. #21462034 | C2 | semidirect |
| 4. #21461628 | C2 | semidirect |
| 5. #21460891 | C2 | semidirect |
| 6. #21460885 | C2 | semidirect |
| 12. #16840803 | C4 | semidirect |
| 13. #16840803 | C4 | semidirect |
| 19. #16840674 | C4 | semidirect |
| 26. #16839576 | C4 | semidirect |
| 27. #16839575 | C4 | semidirect |
| 28. #16839574 | C4 | semidirect |
| 29. C61×#361 | C4 | semidirect |
| 42. D61⋊C16 | C2×C4 | semidirect |
| 43. #14519846 | C2×C4 | semidirect |
| 64. #14519717 | C2×C4 | semidirect |
| 67. #14519713 | C2×C4 | semidirect |
| 70. M32×C61 | C2×C4 | semidirect |
| 71. #108×C61 | C2×C4 | semidirect |
| 204. #361 | #6923 | semidirect |
| 209. C61 | #12647 | semidirect |
| 234. M32 | C2×#6923 | semidirect |
| 239. #108 | C2×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840803 | 2 |
| #21462128 | 2 |
| #21462034 | 2 |
| #21461628 | 2 |
| #21460891 | 2 |
| #21460885 | 2 |
| #361×D61 | 2 |
| #12647 | 61 |