Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
492 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 492 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. #21462004 | C2 | semidirect |
| 3. C4×#14519831 | C2 | semidirect |
| 4. #21461378 | C2 | semidirect |
| 5. #21461168 | C2 | semidirect |
| 20. #16840158 | C4 | semidirect |
| 21. #16840134 | C4 | semidirect |
| 22. #16840113 | C4 | semidirect |
| 26. C61×#486 | C4 | semidirect |
| 141. #92418 | #104 | semidirect |
| 178. #486 | #6923 | semidirect |
| 192. C61 | #9851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462004 | 2 |
| #21461953 | 2 |
| C4×#14519831 | 2 |
| #21461378 | 2 |
| #21461168 | 2 |
| #21461165 | 2 |
| #21456377 | 2 |
| #9851 | 61 |