Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1450 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1450 conjugacy classes of subgroups — too many to draw. Only its 187 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. #26030183 | C2 | semidirect |
| 3. #26021462 | C2 | semidirect |
| 4. #26020700 | C2 | semidirect |
| 5. #26020461 | C2 | semidirect |
| 6. #26020205 | C2 | semidirect |
| 7. #26020173 | C2 | semidirect |
| 8. C89×#2309 | C2 | semidirect |
| 19. #19151638 | C22 | semidirect |
| 20. C2×#15667940 | C22 | semidirect |
| 21. #19151597 | C22 | semidirect |
| 23. C2×#15667929 | C22 | semidirect |
| 24. #19151562 | C22 | semidirect |
| 25. #19151358 | C22 | semidirect |
| 27. C2×#117×C89 | C22 | semidirect |
| 28. C2×#117×C89 | C22 | semidirect |
| 31. #390×C89 | C22 | semidirect |
| 231. #2309 | D89 | semidirect |
| 237. C89 | #24022 | semidirect |
| 247. C2×#117 | C2×D89 | semidirect |
| 248. C2×#117 | C2×D89 | semidirect |
| 259. #390 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033887 | 2 |
| #26030183 | 2 |
| #26021462 | 2 |
| #26020700 | 2 |
| #26020461 | 2 |
| #26020205 | 2 |
| #26020173 | 2 |
| C89×#2309 | 2 |
| #24022 | 89 |