Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
582 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 103 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. C4×#15667927 | C2 | semidirect |
| 3. #26018769 | C2 | semidirect |
| 4. #26018106 | C2 | semidirect |
| 5. C89×#2973 | C2 | semidirect |
| 8. #19151537 | C4 | semidirect |
| 9. #19151534 | C4 | semidirect |
| 10. #19151515 | C4 | semidirect |
| 12. #19151507 | C4 | semidirect |
| 61. C22⋊C8×C89 | D4 | semidirect |
| 204. #2973 | D89 | semidirect |
| 209. C89 | #9185 | semidirect |
| 259. C22⋊C8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026136 | 2 |
| C4×#15667927 | 2 |
| #26018769 | 2 |
| #26018106 | 2 |
| C89×#2973 | 2 |
| #9185 | 89 |