Finite Group DatabasebetaFinite Group DatabasebetaOrder 28736.
234 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 99 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. #28385335 | C2 | semidirect |
| 2. #28385333 | C2 | semidirect |
| 3. #28385330 | C2 | semidirect |
| 4. #28385326 | C2 | semidirect |
| 5. #28385325 | C2 | semidirect |
| 6. #28385322 | C2 | semidirect |
| 7. #28385318 | C2 | semidirect |
| 9. C4×Dic898 | C2 | semidirect |
| 10. C4×D1796 | C2 | semidirect |
| 11. C4×C22⋊D449 | C2 | semidirect |
| 12. C4×C22⋊D449 | C2 | semidirect |
| 13. #28385297 | C2 | semidirect |
| 14. C42×D449 | C2 | semidirect |
| 15. #117×C449 | C2 | semidirect |
| 103. C449 | #529 | semidirect |
| 118. #117 | D449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28385335 | 2 |
| #28385333 | 2 |
| #28385330 | 2 |
| #28385326 | 2 |
| #28385325 | 2 |
| #28385322 | 2 |
| #28385318 | 2 |
| #28385313 | 2 |
| C4×Dic898 | 2 |
| C4×D1796 | 2 |
| C4×C22⋊D449 | 2 |
| #28385297 | 2 |
| C42×D449 | 2 |
| #117×C449 | 2 |
| #529 | 449 |