Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
468 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 96 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. #21461995 | C2 | semidirect |
| 3. C4×#14519845 | C2 | semidirect |
| 4. #21461202 | C2 | semidirect |
| 6. C8×#11758213 | C2 | semidirect |
| 22. #16840160 | C4 | semidirect |
| 23. #16840112 | C4 | semidirect |
| 24. #16840108 | C4 | semidirect |
| 30. C61×#492 | C4 | semidirect |
| 100. #11758213 | SD16 | semidirect |
| 161. C8×C61 | #104 | semidirect |
| 201. #492 | #6923 | semidirect |
| 221. C61 | #9717 | semidirect |
| 354. C8 | #14519841 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461995 | 2 |
| #21461983 | 2 |
| C4×#14519845 | 2 |
| #21461202 | 2 |
| #21461199 | 2 |
| C8×#11758213 | 2 |
| #21456376 | 2 |
| #9717 | 61 |