Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1516 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1516 conjugacy classes of subgroups — too many to draw. Only its 183 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. #26031049 | C2 | semidirect |
| 2. #26025183 | C2 | semidirect |
| 3. #26019272 | C2 | semidirect |
| 4. #26019170 | C2 | semidirect |
| 5. #26018768 | C2 | semidirect |
| 6. #26018579 | C2 | semidirect |
| 7. C2×#534×C89 | C2 | semidirect |
| 9. C2×#15667986 | C22 | semidirect |
| 12. #19151914 | C22 | semidirect |
| 15. #19151731 | C22 | semidirect |
| 16. #19151562 | C22 | semidirect |
| 17. #19151534 | C22 | semidirect |
| 18. #19151507 | C22 | semidirect |
| 20. C4×C22⋊Dic89 | C22 | semidirect |
| 21. #19151332 | C22 | semidirect |
| 22. #19151322 | C22 | semidirect |
| 32. C22×D356 | C23 | semidirect |
| 41. C2×C4⋊Dic89 | C23 | semidirect |
| 52. C22⋊#10623494 | C23 | semidirect |
| 53. #15667919 | C23 | semidirect |
| 62. C22×D4×C89 | D4 | semidirect |
| 72. #121×C89 | D4 | semidirect |
| 77. C2×C4⋊C4×C89 | D4 | semidirect |
| 256. C2×#534 | D89 | semidirect |
| 263. C89 | #18316 | semidirect |
| 299. C22×D4 | C22⋊D89 | semidirect |
| 314. #121 | C22⋊D89 | semidirect |
| 322. C2×C4⋊C4 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031049 | 2 |
| #26025183 | 2 |
| #26019272 | 2 |
| #26019170 | 2 |
| #26018768 | 2 |
| #26018579 | 2 |
| C2×#534×C89 | 2 |
| #18316 | 89 |