Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
380 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 99 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. #364×D89 | C2 | semidirect |
| 3. #26018537 | C2 | semidirect |
| 4. #26018229 | C2 | semidirect |
| 5. #26018228 | C2 | semidirect |
| 6. #26018227 | C2 | semidirect |
| 7. C89×#1336 | C2 | semidirect |
| 20. #19151419 | C22 | semidirect |
| 22. #19151319 | C22 | semidirect |
| 25. #364×C89 | C22 | semidirect |
| 26. #322×C89 | C22 | semidirect |
| 28. #15668035 | C8 | semidirect |
| 32. #15668031 | C8 | semidirect |
| 33. Q16×D89 | C8 | semidirect |
| 35. D8×D89 | C8 | semidirect |
| 187. #1336 | D89 | semidirect |
| 188. C89 | #11604 | semidirect |
| 204. #364 | C2×D89 | semidirect |
| 206. #322 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #443×D89 | 2 |
| #364×D89 | 2 |
| #26018537 | 2 |
| #26018229 | 2 |
| #26018228 | 2 |
| #26018227 | 2 |
| C89×#1336 | 2 |
| #11604 | 89 |