Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1402 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1402 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 |
|---|---|---|
| 2. #26031054 | C2 | semidirect |
| 3. #26019237 | C2 | semidirect |
| 4. #26019203 | C2 | semidirect |
| 5. #26018767 | C2 | semidirect |
| 6. #26018579 | C2 | semidirect |
| 7. C89×#2561 | C2 | semidirect |
| 17. #19151911 | C22 | semidirect |
| 20. #19151737 | C22 | semidirect |
| 21. #19151562 | C22 | semidirect |
| 22. #19151331 | C22 | semidirect |
| 23. #19151322 | C22 | semidirect |
| 24. C2×C22⋊Q8×C89 | C22 | semidirect |
| 26. #397×C89 | C22 | semidirect |
| 27. #393×C89 | C22 | semidirect |
| 31. C4×C22⋊C4×C89 | C22 | semidirect |
| 61. C22⋊#10623494 | C23 | semidirect |
| 63. C22×Q8×C89 | C23 | semidirect |
| 69. C2×C4⋊C4×C89 | C23 | semidirect |
| 81. #95×C89 | C23 | semidirect |
| 238. #2561 | D89 | semidirect |
| 243. C89 | #18317 | semidirect |
| 249. C2×C22⋊Q8 | C2×D89 | semidirect |
| 260. #397 | C2×D89 | semidirect |
| 261. #393 | C2×D89 | semidirect |
| 265. C4×C22⋊C4 | C2×D89 | semidirect |
| 270. C22×Q8 | C22×D89 | semidirect |
| 298. C2×C4⋊C4 | C22×D89 | semidirect |
| 317. #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 |
| #26031054 | 2 |
| #26019237 | 2 |
| #26019203 | 2 |
| #26018767 | 2 |
| #26018579 | 2 |
| C89×#2561 | 2 |
| #18317 | 89 |