Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1516 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1516 conjugacy classes of subgroups — too many to draw. Only its 167 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. C2×#19152160 | C2 | semidirect |
| 2. #26031049 | C2 | semidirect |
| 3. #26019271 | C2 | semidirect |
| 4. #26019169 | C2 | semidirect |
| 5. #26018767 | C2 | semidirect |
| 6. #26018579 | C2 | semidirect |
| 7. C89×#2539 | C2 | semidirect |
| 16. #19151916 | C22 | semidirect |
| 19. #19151732 | C22 | semidirect |
| 21. #19151562 | C22 | semidirect |
| 22. #19151331 | C22 | semidirect |
| 23. #19151322 | C22 | semidirect |
| 25. C2×#121×C89 | C22 | semidirect |
| 28. #399×C89 | C22 | semidirect |
| 29. #392×C89 | C22 | semidirect |
| 31. C4×C22⋊C4×C89 | C22 | semidirect |
| 34. C22×D356 | D4 | semidirect |
| 49. #15667986 | D4 | semidirect |
| 54. C2×C4⋊Dic89 | D4 | semidirect |
| 61. C22⋊#10623494 | C23 | semidirect |
| 65. C22×D4×C89 | C23 | semidirect |
| 73. C2×C4⋊C4×C89 | C23 | semidirect |
| 83. #95×C89 | C23 | semidirect |
| 258. #2539 | D89 | semidirect |
| 263. C89 | #18316 | semidirect |
| 272. C2×#121 | C2×D89 | semidirect |
| 282. #399 | C2×D89 | semidirect |
| 283. #392 | C2×D89 | semidirect |
| 285. C4×C22⋊C4 | C2×D89 | semidirect |
| 299. C22×D4 | C22×D89 | semidirect |
| 322. C2×C4⋊C4 | C22×D89 | semidirect |
| 339. #95 | C22×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152160 | 2 |
| #26031049 | 2 |
| #26019271 | 2 |
| #26019169 | 2 |
| #26018767 | 2 |
| #26018579 | 2 |
| C89×#2539 | 2 |
| #18316 | 89 |