Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
864 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 864 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 1. #26021081 | C2 | semidirect |
| 2. C4×#15667939 | C2 | semidirect |
| 3. #26018844 | C2 | semidirect |
| 4. #26018691 | C2 | semidirect |
| 15. Q82×C89 | C4 | semidirect |
| 18. #555×C89 | C4 | semidirect |
| 20. #550×C89 | C4 | semidirect |
| 135. Q8×C89 | #104 | semidirect |
| 200. C89 | #8441 | semidirect |
| 201. Q82 | Dic89 | semidirect |
| 204. #555 | Dic89 | semidirect |
| 206. #550 | Dic89 | semidirect |
| 330. Q8 | #15667939 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021081 | 2 |
| C4×#15667939 | 2 |
| #26018844 | 2 |
| #26018691 | 2 |
| C89×#3483 | 2 |
| #8441 | 89 |