Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
438 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 438 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 |
|---|---|---|
| 3. #26018785 | C2 | semidirect |
| 4. #26018616 | C2 | semidirect |
| 5. #26018161 | C2 | semidirect |
| 6. #26018128 | C2 | semidirect |
| 27. #484×C89 | C4 | semidirect |
| 28. #481×C89 | C4 | semidirect |
| 32. #451×C89 | C4 | semidirect |
| 33. #448×C89 | C4 | semidirect |
| 224. C89 | #9331 | semidirect |
| 228. #484 | Dic89 | semidirect |
| 229. #481 | Dic89 | semidirect |
| 233. #451 | Dic89 | semidirect |
| 234. #448 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029314 | 2 |
| #26018808 | 2 |
| #26018785 | 2 |
| #26018616 | 2 |
| #26018161 | 2 |
| #26018128 | 2 |
| C89×#3196 | 2 |
| #9331 | 89 |