Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
498 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26029393 | C2 | semidirect |
| 3. #26021179 | C2 | semidirect |
| 4. #26018965 | C2 | semidirect |
| 5. #26018775 | C2 | semidirect |
| 6. #26018121 | C2 | semidirect |
| 7. C89×#1285 | C2 | semidirect |
| 10. #19151987 | C4 | semidirect |
| 11. #19151963 | C4 | semidirect |
| 222. #1285 | D89 | semidirect |
| 223. C89 | #9378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031272 | 2 |
| #26029393 | 2 |
| #26021179 | 2 |
| #26018965 | 2 |
| #26018775 | 2 |
| #26018121 | 2 |
| C89×#1285 | 2 |
| #9378 | 89 |