Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
438 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26029241 | C2 | semidirect |
| 3. #26018873 | C2 | semidirect |
| 4. C2×#19151338 | C2 | semidirect |
| 5. #26018150 | C2 | semidirect |
| 6. #26018096 | C2 | semidirect |
| 7. C89×#1469 | C2 | semidirect |
| 217. #1469 | D89 | semidirect |
| 220. C89 | #9265 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031217 | 2 |
| #26029241 | 2 |
| #26018873 | 2 |
| C2×#19151338 | 2 |
| #26018150 | 2 |
| #26018096 | 2 |
| C89×#1469 | 2 |
| #9265 | 89 |