Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
186 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 186 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 |
|---|---|---|
| 2. #366×D89 | C2 | semidirect |
| 3. #26018451 | C2 | semidirect |
| 4. #26018431 | C2 | semidirect |
| 5. #26018429 | C2 | semidirect |
| 6. #26018389 | C2 | semidirect |
| 7. C89×#1423 | C2 | semidirect |
| 92. #1423 | D89 | semidirect |
| 96. C89 | #13711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022339 | 2 |
| #366×D89 | 2 |
| #26018451 | 2 |
| #26018431 | 2 |
| #26018429 | 2 |
| #26018389 | 2 |
| C89×#1423 | 2 |
| #13711 | 89 |