Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
464 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 81 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. #26031468 | C2 | semidirect |
| 4. #26021232 | C2 | semidirect |
| 5. #26018765 | C2 | semidirect |
| 7. C89×#1307 | C2 | semidirect |
| 198. #1307 | D89 | semidirect |
| 199. C89 | #10215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031640 | 2 |
| #26031468 | 2 |
| #26031265 | 2 |
| #26021232 | 2 |
| #26018765 | 2 |
| #26018761 | 2 |
| C89×#1307 | 2 |
| #10215 | 89 |