Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
702 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 107 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. C22×#15667931 | C2 | semidirect |
| 3. C2×#19151394 | C2 | semidirect |
| 4. #26018378 | C2 | semidirect |
| 5. C89×#1784 | C2 | semidirect |
| 48. #15667931 | D4 | semidirect |
| 205. C22×C89 | #355 | semidirect |
| 236. #1784 | D89 | semidirect |
| 238. C89 | #13092 | semidirect |
| 443. C22 | #19151394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667931 | 2 |
| #26023906 | 2 |
| C2×#19151394 | 2 |
| #26018378 | 2 |
| C89×#1784 | 2 |
| #13092 | 89 |