Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
912 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26029278 | C2 | semidirect |
| 3. #26020237 | C2 | semidirect |
| 4. #26020184 | C2 | semidirect |
| 5. #26020182 | C2 | semidirect |
| 6. #26018119 | C2 | semidirect |
| 7. C89×#1289 | C2 | semidirect |
| 20. #19151516 | C4 | semidirect |
| 21. #19151508 | C4 | semidirect |
| 41. C22×#10623494 | D4 | semidirect |
| 68. C22×C8×C89 | D4 | semidirect |
| 286. #1289 | D89 | semidirect |
| 287. C89 | #9472 | semidirect |
| 323. C22×C8 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029278 | 2 |
| #26023609 | 2 |
| #26020237 | 2 |
| #26020184 | 2 |
| #26020182 | 2 |
| #26018119 | 2 |
| C89×#1289 | 2 |
| #9472 | 89 |