Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
544 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26028971 | C2 | semidirect |
| 3. #26018902 | C2 | semidirect |
| 4. #26018677 | C2 | semidirect |
| 5. #26018149 | C2 | semidirect |
| 6. #26018097 | C2 | semidirect |
| 7. C89×#1955 | C2 | semidirect |
| 117. C2×C8×C89 | D8 | semidirect |
| 210. #1955 | D89 | semidirect |
| 215. C89 | #9049 | semidirect |
| 321. C2×C8 | #13083559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030252 | 2 |
| #26028971 | 2 |
| #26018902 | 2 |
| #26018677 | 2 |
| #26018149 | 2 |
| #26018097 | 2 |
| C89×#1955 | 2 |
| #9049 | 89 |