Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1152 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 1152 conjugacy classes of subgroups — too many to draw. Only its 155 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×#19152340 | C2 | semidirect |
| 2. #26031235 | C2 | semidirect |
| 3. #26019556 | C2 | semidirect |
| 4. #26019540 | C2 | semidirect |
| 5. #26018876 | C2 | semidirect |
| 6. #26018849 | C2 | semidirect |
| 7. C89×#3153 | C2 | semidirect |
| 16. #19151985 | C22 | semidirect |
| 17. #19151960 | C22 | semidirect |
| 21. #19151655 | C22 | semidirect |
| 22. #19151338 | C22 | semidirect |
| 23. #19151337 | C22 | semidirect |
| 26. #532×C89 | C22 | semidirect |
| 28. #497×C89 | C22 | semidirect |
| 29. #496×C89 | C22 | semidirect |
| 31. C4×M16×C89 | C22 | semidirect |
| 60. #15667923 | C23 | semidirect |
| 71. C4⋊Q8×C89 | C23 | semidirect |
| 72. #127×C89 | C23 | semidirect |
| 81. #97×C89 | C23 | semidirect |
| 209. #3153 | D89 | semidirect |
| 214. C89 | #18992 | semidirect |
| 220. #532 | C2×D89 | semidirect |
| 227. #497 | C2×D89 | semidirect |
| 229. #496 | C2×D89 | semidirect |
| 236. C4×M16 | C2×D89 | semidirect |
| 256. C4⋊Q8 | C22×D89 | semidirect |
| 257. #127 | C22×D89 | semidirect |
| 288. #97 | C22×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152340 | 2 |
| #26031235 | 2 |
| #26019556 | 2 |
| #26019540 | 2 |
| #26018876 | 2 |
| #26018849 | 2 |
| C89×#3153 | 2 |
| #18992 | 89 |