Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
924 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 163 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. #26031635 | C2 | semidirect |
| 3. #26019533 | C2 | semidirect |
| 4. #26019484 | C2 | semidirect |
| 5. #26018990 | C2 | semidirect |
| 6. #26018704 | C2 | semidirect |
| 7. C89×#3160 | C2 | semidirect |
| 165. #3160 | D89 | semidirect |
| 170. C89 | #18701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034652 | 2 |
| #26031635 | 2 |
| #26019533 | 2 |
| #26019484 | 2 |
| #26018990 | 2 |
| #26018704 | 2 |
| C89×#3160 | 2 |
| #18701 | 89 |