Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
368 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 65 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. #26022523 | C2 | semidirect |
| 3. #26022303 | C2 | semidirect |
| 4. #26019741 | C2 | semidirect |
| 5. #26018296 | C2 | semidirect |
| 6. #26018223 | C2 | semidirect |
| 7. C89×#1330 | C2 | semidirect |
| 172. #1330 | D89 | semidirect |
| 173. C89 | #12327 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031910 | 2 |
| #26022523 | 2 |
| #26022303 | 2 |
| #26019741 | 2 |
| #26018296 | 2 |
| #26018223 | 2 |
| C89×#1330 | 2 |
| #12327 | 89 |