Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1026 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 1026 conjugacy classes of subgroups — too many to draw. Only its 119 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. #26018945 | C2 | semidirect |
| 3. #26018862 | C2 | semidirect |
| 4. #26018593 | C2 | semidirect |
| 5. C89×#1955 | C2 | semidirect |
| 14. #19151655 | C22 | semidirect |
| 20. C2×C4⋊C8×C89 | C22 | semidirect |
| 22. C2×#97×C89 | C22 | semidirect |
| 170. #1955 | D89 | semidirect |
| 174. C89 | #8456 | semidirect |
| 185. C2×C4⋊C8 | C2×D89 | semidirect |
| 187. C2×#97 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034016 | 2 |
| #26018945 | 2 |
| #26018862 | 2 |
| #26018593 | 2 |
| C89×#1955 | 2 |
| #8456 | 89 |