Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
496 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26026373 | C2 | semidirect |
| 4. #26018970 | C2 | semidirect |
| 6. #26018146 | C2 | semidirect |
| 7. C89×#1528 | C2 | semidirect |
| 178. #1528 | D89 | semidirect |
| 181. C89 | #10093 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031442 | 2 |
| #26030646 | 2 |
| #26026373 | 2 |
| #26018970 | 2 |
| #26018761 | 2 |
| #26018146 | 2 |
| C89×#1528 | 2 |
| #10093 | 89 |