Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
846 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 846 conjugacy classes of subgroups — too many to draw. Only its 184 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. #21462541 | C2 | semidirect |
| 2. #21461953 | C2 | semidirect |
| 3. #21461810 | C2 | semidirect |
| 4. #21461743 | C2 | semidirect |
| 5. #21461532 | C2 | semidirect |
| 21. #16840145 | C4 | semidirect |
| 22. #16840142 | C4 | semidirect |
| 23. #16840134 | C4 | semidirect |
| 25. C61×#493 | C4 | semidirect |
| 154. #493 | #6923 | semidirect |
| 168. C61 | #22280 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462541 | 2 |
| #21461953 | 2 |
| #21461810 | 2 |
| #21461743 | 2 |
| #21461532 | 2 |
| #21456246 | 2 |
| #22280 | 61 |