Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
632 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26022975 | C2 | semidirect |
| 3. #26021085 | C2 | semidirect |
| 4. #26018919 | C2 | semidirect |
| 5. #26018110 | C2 | semidirect |
| 6. #26018080 | C2 | semidirect |
| 7. C89×#1517 | C2 | semidirect |
| 10. #19151974 | C4 | semidirect |
| 11. #19151946 | C4 | semidirect |
| 51. C4×#10623494 | C2×C4 | semidirect |
| 55. C4⋊Q8×C89 | C2×C4 | semidirect |
| 56. #127×C89 | C2×C4 | semidirect |
| 98. C4×Dic89 | D8 | semidirect |
| 216. #1517 | D89 | semidirect |
| 219. C89 | #9299 | semidirect |
| 246. C4⋊Q8 | C4×D89 | semidirect |
| 251. #127 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031167 | 2 |
| #26022975 | 2 |
| #26021085 | 2 |
| #26018919 | 2 |
| #26018110 | 2 |
| #26018080 | 2 |
| C89×#1517 | 2 |
| #9299 | 89 |