Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
502 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 98 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. #21461613 | C2 | semidirect |
| 2. #21461367 | C2 | semidirect |
| 3. #21461199 | C2 | semidirect |
| 4. #21461125 | C2 | semidirect |
| 20. #16840142 | C4 | semidirect |
| 21. #16840134 | C4 | semidirect |
| 23. C61×#493 | C4 | semidirect |
| 172. #493 | #6923 | semidirect |
| 184. C61 | #9753 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461613 | 2 |
| #21461367 | 2 |
| #21461199 | 2 |
| #21461125 | 2 |
| #21456246 | 2 |
| #9753 | 61 |