Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
396 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 78 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. #21461537 | C2 | semidirect |
| 2. #21461380 | C2 | semidirect |
| 3. #21461293 | C2 | semidirect |
| 5. #21461213 | C2 | semidirect |
| 22. #16840158 | C4 | semidirect |
| 23. #16840134 | C4 | semidirect |
| 24. #16840113 | C4 | semidirect |
| 30. C61×#486 | C4 | semidirect |
| 189. #486 | #6923 | semidirect |
| 207. C61 | #9766 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461537 | 2 |
| #21461380 | 2 |
| #21461293 | 2 |
| #21461289 | 2 |
| #21461213 | 2 |
| #21461208 | 2 |
| #21456377 | 2 |
| #9766 | 61 |