Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
440 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 86 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. #21461475 | C2 | semidirect |
| 2. #21461380 | C2 | semidirect |
| 3. #21461292 | C2 | semidirect |
| 5. #21461211 | C2 | semidirect |
| 22. #16840160 | C4 | semidirect |
| 23. #16840112 | C4 | semidirect |
| 24. #16840108 | C4 | semidirect |
| 30. C61×#492 | C4 | semidirect |
| 189. #492 | #6923 | semidirect |
| 209. C61 | #9761 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461475 | 2 |
| #21461380 | 2 |
| #21461292 | 2 |
| #21461289 | 2 |
| #21461211 | 2 |
| #21461208 | 2 |
| #21456376 | 2 |
| #9761 | 61 |