Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
502 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 104 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. #21461756 | C2 | semidirect |
| 2. #21461250 | C2 | semidirect |
| 3. #21461248 | C2 | semidirect |
| 4. #21461023 | C2 | semidirect |
| 20. #16840141 | C4 | semidirect |
| 21. #16840138 | C4 | semidirect |
| 22. #16840135 | C4 | semidirect |
| 24. C61×#492 | C4 | semidirect |
| 188. #492 | #6923 | semidirect |
| 198. C61 | #9756 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461756 | 2 |
| #21461250 | 2 |
| #21461248 | 2 |
| #21461023 | 2 |
| #21456242 | 2 |
| #9756 | 61 |