Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
452 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 3. #26018276 | C2 | semidirect |
| 4. #26018273 | C2 | semidirect |
| 12. C2×C22⋊Q8×C89 | C4 | semidirect |
| 14. #400×C89 | C4 | semidirect |
| 16. #395×C89 | C4 | semidirect |
| 22. C2×#95×C89 | C4 | semidirect |
| 191. C89 | #11902 | semidirect |
| 192. C2×C22⋊Q8 | Dic89 | semidirect |
| 196. #400 | Dic89 | semidirect |
| 198. #395 | Dic89 | semidirect |
| 205. C2×#95 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020240 | 2 |
| #26018573 | 2 |
| #26018276 | 2 |
| #26018273 | 2 |
| C89×#2564 | 2 |
| #11902 | 89 |