Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
574 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26022617 | C2 | semidirect |
| 4. #26018699 | C2 | semidirect |
| 5. #26018144 | C2 | semidirect |
| 6. #26018109 | C2 | semidirect |
| 24. #477×C89 | C4 | semidirect |
| 25. #460×C89 | C4 | semidirect |
| 122. Q8×C89 | #104 | semidirect |
| 191. C89 | #9326 | semidirect |
| 196. #477 | Dic89 | semidirect |
| 197. #460 | Dic89 | semidirect |
| 306. Q8 | #15667939 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022617 | 2 |
| #26021172 | 2 |
| #26018760 | 2 |
| #26018699 | 2 |
| #26018144 | 2 |
| #26018109 | 2 |
| C89×#3112 | 2 |
| #9326 | 89 |