Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1102 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 207 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. #430×D89 | C2 | semidirect |
| 3. #26021769 | C2 | semidirect |
| 4. #26021768 | C2 | semidirect |
| 5. #26021767 | C2 | semidirect |
| 6. #338×D89 | C2 | semidirect |
| 7. C89×#2091 | C2 | semidirect |
| 11. #19151647 | C22 | semidirect |
| 12. #19151646 | C22 | semidirect |
| 20. #19151356 | C22 | semidirect |
| 21. #430×C89 | C22 | semidirect |
| 23. #338×C89 | C22 | semidirect |
| 162. D89 | #2091 | direct (N × H) |
| 168. #2091 | D89 | direct (N × H) |
| 170. C89 | C2×#2091 | semidirect |
| 177. #430 | C2×D89 | semidirect |
| 186. #338 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #430×D89 | 2 |
| #407×D89 | 2 |
| #26021769 | 2 |
| #26021768 | 2 |
| #26021767 | 2 |
| #338×D89 | 2 |
| C89×#2091 | 2 |
| C2×#2091 | 89 |