Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
390 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 78 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. #21462182 | C2 | semidirect |
| 2. C4×#14519845 | C2 | semidirect |
| 3. #21460806 | C2 | semidirect |
| 4. #21460805 | C2 | semidirect |
| 13. #16840166 | C4 | semidirect |
| 14. #16840137 | C4 | semidirect |
| 19. C4×D488 | C4 | semidirect |
| 22. C4×D8×C61 | C4 | semidirect |
| 167. C4×D8 | #6923 | semidirect |
| 175. C61 | #11744 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462182 | 2 |
| C4×#14519845 | 2 |
| #21460806 | 2 |
| #21460805 | 2 |
| #21456395 | 2 |
| #11744 | 61 |