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.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D449 |
| commutator, socle, cosocle | C22×C449 | C24 |
| Fitting | #123×C449 | C2 |
| prime radical | #28385312 | C2 |
| hypercenter | #123 | D449 |
| hypocenter | C449 | #529 |
| LCS | G ▷ C22×C449 ▷ C449 | |
| UCS | C1 ◁ C22 ◁ #123 | |
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. #28385323 | C2 | semidirect |
| 6. #28385317 | C2 | semidirect |
| 8. #28385305 | C2 | semidirect |
| 9. D4×Dic449 | C2 | semidirect |
| 10. #28385300 | C2 | semidirect |
| 11. #28385300 | C2 | semidirect |
| 12. #28385298 | C2 | semidirect |
| 13. #28385296 | C2 | semidirect |
| 14. C2×C4×Dic449 | C2 | semidirect |
| 15. #123×C449 | C2 | semidirect |
| 103. C449 | #529 | semidirect |
| 110. #123 | 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 |
| #28385323 | 2 |
| #28385317 | 2 |
| #28385312 | 2 |
| #28385305 | 2 |
| D4×Dic449 | 2 |
| #28385300 | 2 |
| #28385298 | 2 |
| #28385296 | 2 |
| C2×C4×Dic449 | 2 |
| #123×C449 | 2 |
| #529 | 449 |