Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
762 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 762 conjugacy classes of subgroups — too many to draw. Only its 131 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. #26018819 | C2 | semidirect |
| 3. C2×#19151322 | C2 | semidirect |
| 4. #26018119 | C2 | semidirect |
| 5. C89×#2315 | C2 | semidirect |
| 9. #19151523 | C4 | semidirect |
| 11. #19151507 | C4 | semidirect |
| 21. C22×D356 | C2×C4 | semidirect |
| 30. C2×C4⋊Dic89 | C2×C4 | semidirect |
| 38. #15667919 | C2×C4 | semidirect |
| 54. #95×C89 | D4 | semidirect |
| 216. #2315 | D89 | semidirect |
| 220. C89 | #9203 | semidirect |
| 269. #95 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025986 | 2 |
| #26018819 | 2 |
| C2×#19151322 | 2 |
| #26018119 | 2 |
| C89×#2315 | 2 |
| #9203 | 89 |