Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
398 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 55 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. #26028081 | C2 | semidirect |
| 2. #26019289 | C2 | semidirect |
| 4. #26018278 | C2 | semidirect |
| 5. #26018254 | C2 | semidirect |
| 6. #26018198 | C2 | semidirect |
| 7. C89×#2039 | C2 | semidirect |
| 192. #2039 | D89 | semidirect |
| 198. C89 | #12144 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028081 | 2 |
| #26019289 | 2 |
| #26019187 | 2 |
| #26018278 | 2 |
| #26018254 | 2 |
| #26018198 | 2 |
| C89×#2039 | 2 |
| #12144 | 89 |