Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1630 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1630 conjugacy classes of subgroups — too many to draw. Only its 171 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. #26030347 | C2 | semidirect |
| 3. #26019428 | C2 | semidirect |
| 4. #26018966 | C2 | semidirect |
| 5. #26018696 | C2 | semidirect |
| 6. C89×#3138 | C2 | semidirect |
| 15. #19151875 | C22 | semidirect |
| 16. #19151800 | C22 | semidirect |
| 19. #19151655 | C22 | semidirect |
| 20. #19151342 | C22 | semidirect |
| 21. #19151327 | C22 | semidirect |
| 22. #533×C89 | C22 | semidirect |
| 25. #486×C89 | C22 | semidirect |
| 27. C4×M16×C89 | C22 | semidirect |
| 48. C4⋊#10623494 | C23 | semidirect |
| 56. C4⋊Q8×C89 | C23 | semidirect |
| 67. C4×C8×C89 | C23 | semidirect |
| 168. #3138 | D89 | semidirect |
| 173. C89 | #18529 | semidirect |
| 178. #533 | C2×D89 | semidirect |
| 184. #486 | C2×D89 | semidirect |
| 192. C4×M16 | C2×D89 | semidirect |
| 206. C4⋊Q8 | C22×D89 | semidirect |
| 234. C4×C8 | C22×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152233 | 2 |
| #26030347 | 2 |
| #26019428 | 2 |
| #26018966 | 2 |
| #26018696 | 2 |
| C89×#3138 | 2 |
| #18529 | 89 |