Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1486 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1486 conjugacy classes of subgroups — too many to draw. Only its 187 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. #26031000 | C2 | semidirect |
| 3. #26019237 | C2 | semidirect |
| 4. #26019169 | C2 | semidirect |
| 5. #26018819 | C2 | semidirect |
| 6. C2×#19151322 | C2 | semidirect |
| 7. C89×#2617 | C2 | semidirect |
| 16. #19151911 | C22 | semidirect |
| 19. #19151732 | C22 | semidirect |
| 21. C2×C22⋊#10623494 | C22 | semidirect |
| 22. #19151331 | C22 | semidirect |
| 23. #19151322 | C22 | semidirect |
| 24. C2×#121×C89 | C22 | semidirect |
| 27. #397×C89 | C22 | semidirect |
| 29. #392×C89 | C22 | semidirect |
| 31. #380×C89 | C22 | semidirect |
| 34. C22×D356 | D4 | semidirect |
| 50. #15667986 | D4 | semidirect |
| 55. C2×C4⋊Dic89 | D4 | semidirect |
| 62. C22⋊#10623494 | C23 | semidirect |
| 66. C22×D4×C89 | C23 | semidirect |
| 73. C2×C4⋊C4×C89 | C23 | semidirect |
| 83. #95×C89 | C23 | semidirect |
| 121. C24×C89 | D8 | semidirect |
| 265. #2617 | D89 | semidirect |
| 270. C89 | #18284 | semidirect |
| 278. C2×#121 | C2×D89 | semidirect |
| 288. #397 | C2×D89 | semidirect |
| 290. #392 | C2×D89 | semidirect |
| 292. #380 | C2×D89 | semidirect |
| 307. C22×D4 | C22×D89 | semidirect |
| 329. C2×C4⋊C4 | C22×D89 | semidirect |
| 346. #95 | C22×D89 | semidirect |
| 358. C24 | #13083559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152160 | 2 |
| #26031000 | 2 |
| #26019237 | 2 |
| #26019169 | 2 |
| #26018819 | 2 |
| C2×#19151322 | 2 |
| C89×#2617 | 2 |
| #18284 | 89 |