Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
440 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 69 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. #26021923 | C2 | semidirect |
| 3. #26021902 | C2 | semidirect |
| 4. #26020799 | C2 | semidirect |
| 5. #26020538 | C2 | semidirect |
| 6. #26018380 | C2 | semidirect |
| 7. C89×#1910 | C2 | semidirect |
| 206. #1910 | D89 | semidirect |
| 209. C89 | #13432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031113 | 2 |
| #26021923 | 2 |
| #26021902 | 2 |
| #26020799 | 2 |
| #26020538 | 2 |
| #26018380 | 2 |
| C89×#1910 | 2 |
| #13432 | 89 |