Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
488 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 113 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×#15667951 | C2 | semidirect |
| 3. C2×#19151405 | C2 | semidirect |
| 4. #26020287 | C2 | semidirect |
| 5. #26018349 | C2 | semidirect |
| 6. #26018348 | C2 | semidirect |
| 7. C2×#359×C89 | C2 | semidirect |
| 45. C2×#13083549 | D4 | semidirect |
| 65. C2×C16×C89 | D4 | semidirect |
| 184. C2×#359 | D89 | semidirect |
| 188. C89 | #13064 | semidirect |
| 239. C2×C16 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667951 | 2 |
| #26029829 | 2 |
| C2×#19151405 | 2 |
| #26020287 | 2 |
| #26018349 | 2 |
| #26018348 | 2 |
| C2×#359×C89 | 2 |
| #13064 | 89 |