Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
538 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 90 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. #21462565 | C2 | semidirect |
| 2. #21461982 | C2 | semidirect |
| 3. #21461200 | C2 | semidirect |
| 4. #21461126 | C2 | semidirect |
| 5. #21460654 | C2 | semidirect |
| 6. #21460651 | C2 | semidirect |
| 24. #16840139 | C4 | semidirect |
| 25. #16840110 | C4 | semidirect |
| 26. #16840110 | C4 | semidirect |
| 30. C61×#500 | C4 | semidirect |
| 115. #11758213 | D8 | semidirect |
| 226. #500 | #6923 | semidirect |
| 246. C61 | #9053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462565 | 2 |
| #21461982 | 2 |
| #21461200 | 2 |
| #21461126 | 2 |
| #21460654 | 2 |
| #21460651 | 2 |
| #21456399 | 2 |
| #9053 | 61 |