Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
494 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 116 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. #21460862 | C2 | semidirect |
| 15. #16840659 | C4 | semidirect |
| 16. #16840658 | C4 | semidirect |
| 21. #16839544 | C4 | semidirect |
| 22. #16839543 | C4 | semidirect |
| 23. C61×#349 | C4 | semidirect |
| 38. #14519851 | C2×C4 | semidirect |
| 54. #14519717 | C2×C4 | semidirect |
| 58. M32×C61 | C2×C4 | semidirect |
| 188. #349 | #6923 | semidirect |
| 191. C61 | #12607 | semidirect |
| 218. M32 | C2×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×#6923 | 2 |
| D61⋊#349 | 2 |
| #21462034 | 2 |
| #21460862 | 2 |
| #349×D61 | 2 |
| #12607 | 61 |