Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
2070 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 2070 conjugacy classes of subgroups — too many to draw. Only its 501 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D89 |
| commutator, socle, cosocle | C23×C89 | C25 |
| Fitting | C89×#2840 | C2 |
| hypercenter | #2840 | D89 |
| hypocenter | C89 | #36675 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #2840 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26028443 | C2 | semidirect |
| 2. #26028336 | C2 | semidirect |
| 3. #26028249 | C2 | semidirect |
| 4. #26023534 | C2 | semidirect |
| 5. #26023469 | C2 | semidirect |
| 6. #26022751 | C2 | semidirect |
| 7. C89×#2840 | C2 | semidirect |
| 8. C22×#13083575 | C22 | semidirect |
| 11. C2×Q8×Dic89 | C22 | semidirect |
| 13. #19151540 | C22 | semidirect |
| 14. #19151525 | C22 | semidirect |
| 16. #19151517 | C22 | semidirect |
| 17. #19151516 | C22 | semidirect |
| 19. #19151509 | C22 | semidirect |
| 24. #19151445 | C22 | semidirect |
| 25. #19151443 | C22 | semidirect |
| 76. C24×C89 | #41 | semidirect |
| 131. #2840 | D89 | semidirect |
| 138. C89 | #36675 | semidirect |
| 189. C24 | #13083575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028443 | 2 |
| #26028336 | 2 |
| #26028249 | 2 |
| #26023534 | 2 |
| #26023469 | 2 |
| #26022751 | 2 |
| C89×#2840 | 2 |
| #36675 | 89 |