Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
574 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 574 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. #26031179 | C2 | semidirect |
| 3. #26030711 | C2 | semidirect |
| 4. #26021240 | C2 | semidirect |
| 5. #26018843 | C2 | semidirect |
| 6. #26018668 | C2 | semidirect |
| 7. C89×#1299 | C2 | semidirect |
| 195. #1299 | D89 | semidirect |
| 196. C89 | #10106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031633 | 2 |
| #26031179 | 2 |
| #26030711 | 2 |
| #26021240 | 2 |
| #26018843 | 2 |
| #26018668 | 2 |
| C89×#1299 | 2 |
| #10106 | 89 |