Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
506 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 96 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. #21461983 | C2 | semidirect |
| 2. C4×#14519846 | C2 | semidirect |
| 3. #21461199 | C2 | semidirect |
| 4. C8×#11758213 | C2 | semidirect |
| 16. #16840167 | C4 | semidirect |
| 17. #16840108 | C4 | semidirect |
| 23. C61×#493 | C4 | semidirect |
| 74. #11758213 | D8 | semidirect |
| 119. C8×C61 | #104 | semidirect |
| 153. #493 | #6923 | semidirect |
| 169. C61 | #9719 | semidirect |
| 267. C8 | #14519841 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461983 | 2 |
| C4×#14519846 | 2 |
| #21461199 | 2 |
| C8×#11758213 | 2 |
| #21456396 | 2 |
| #9719 | 61 |