Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1066 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 1066 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 |
|---|---|---|
| 2. #26031251 | C2 | semidirect |
| 3. #26019557 | C2 | semidirect |
| 4. #26018876 | C2 | semidirect |
| 5. #26018849 | C2 | semidirect |
| 6. C89×#3140 | C2 | semidirect |
| 15. #19151990 | C22 | semidirect |
| 16. #19151960 | C22 | semidirect |
| 20. #19151655 | C22 | semidirect |
| 21. #19151338 | C22 | semidirect |
| 22. #19151337 | C22 | semidirect |
| 23. #533×C89 | C22 | semidirect |
| 25. #489×C89 | C22 | semidirect |
| 29. C4×M16×C89 | C22 | semidirect |
| 58. #15667923 | C23 | semidirect |
| 62. C4⋊Q8×C89 | C23 | semidirect |
| 74. #97×C89 | C23 | semidirect |
| 185. #3140 | D89 | semidirect |
| 189. C89 | #18997 | semidirect |
| 193. #533 | C2×D89 | semidirect |
| 202. #489 | C2×D89 | semidirect |
| 210. C4×M16 | C2×D89 | semidirect |
| 223. C4⋊Q8 | C22×D89 | semidirect |
| 257. #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 |
| #26031251 | 2 |
| #26019557 | 2 |
| #26018876 | 2 |
| #26018849 | 2 |
| C89×#3140 | 2 |
| #18997 | 89 |