Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
498 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 92 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. #21461982 | C2 | semidirect |
| 2. C4×#14519845 | C2 | semidirect |
| 3. #21461200 | C2 | semidirect |
| 4. #21461029 | C2 | semidirect |
| 16. #16840139 | C4 | semidirect |
| 17. #16840110 | C4 | semidirect |
| 23. C61×#500 | C4 | semidirect |
| 117. C8×C61 | #104 | semidirect |
| 148. #500 | #6923 | semidirect |
| 165. C61 | #9721 | semidirect |
| 261. C8 | #14519842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461982 | 2 |
| C4×#14519845 | 2 |
| #21461200 | 2 |
| #21461029 | 2 |
| #21456399 | 2 |
| #9721 | 61 |