Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
498 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26029391 | C2 | semidirect |
| 3. #26021179 | C2 | semidirect |
| 4. #26018965 | C2 | semidirect |
| 5. #26018121 | C2 | semidirect |
| 6. #26018108 | C2 | semidirect |
| 7. C89×#1509 | C2 | semidirect |
| 9. #19151988 | C4 | semidirect |
| 10. #19151964 | C4 | semidirect |
| 220. #1509 | 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 |
|---|---|
| #26031267 | 2 |
| #26029391 | 2 |
| #26021179 | 2 |
| #26018965 | 2 |
| #26018121 | 2 |
| #26018108 | 2 |
| C89×#1509 | 2 |
| #9378 | 89 |