Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
996 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 179 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. #21457206 | C2 | semidirect |
| 2. #21456141 | C2 | semidirect |
| 3. #21445047 | C2 | semidirect |
| 4. #21444998 | C2 | semidirect |
| 5. #21444554 | C2 | semidirect |
| 6. #21444270 | C2 | semidirect |
| 8. #16840319 | C22 | semidirect |
| 10. #16840112 | C22 | semidirect |
| 13. #16840042 | C22 | semidirect |
| 15. #16839967 | C22 | semidirect |
| 17. #16839786 | C22 | semidirect |
| 19. C2×C4×#92418 | C22 | semidirect |
| 20. #16839511 | C22 | semidirect |
| 22. D4⋊#92418 | C22 | semidirect |
| 211. C61 | #18691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21457206 | 2 |
| #21456141 | 2 |
| #21445047 | 2 |
| #21444998 | 2 |
| #21444554 | 2 |
| #21444270 | 2 |
| C61×#3549 | 2 |
| #18691 | 61 |