Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
580 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 91 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. #26029291 | C2 | semidirect |
| 3. C4×#15667926 | C2 | semidirect |
| 4. #26018768 | C2 | semidirect |
| 5. #26018106 | C2 | semidirect |
| 6. #26018105 | C2 | semidirect |
| 7. C89×#1507 | C2 | semidirect |
| 15. #19151536 | C4 | semidirect |
| 16. #19151533 | C4 | semidirect |
| 18. #19151512 | C4 | semidirect |
| 20. #19151506 | C4 | semidirect |
| 55. C22⋊#10623494 | D4 | semidirect |
| 77. C22⋊C8×C89 | D4 | semidirect |
| 256. #1507 | D89 | semidirect |
| 259. C89 | #9186 | semidirect |
| 322. C22⋊C8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029291 | 2 |
| #26026137 | 2 |
| C4×#15667926 | 2 |
| #26018768 | 2 |
| #26018106 | 2 |
| #26018105 | 2 |
| C89×#1507 | 2 |
| #9186 | 89 |