Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
476 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26031023 | C2 | semidirect |
| 2. #26022181 | C2 | semidirect |
| 4. #26018265 | C2 | semidirect |
| 5. #26018264 | C2 | semidirect |
| 6. #26018175 | C2 | semidirect |
| 7. C89×#2187 | C2 | semidirect |
| 30. C2×Dic356 | D4 | semidirect |
| 47. #15667946 | D4 | semidirect |
| 56. C2×Q16×C89 | D4 | semidirect |
| 64. #107×C89 | D4 | semidirect |
| 131. C22×D89 | SD32 | semidirect |
| 199. #2187 | D89 | semidirect |
| 204. C89 | #12103 | semidirect |
| 230. C2×Q16 | C22⋊D89 | semidirect |
| 255. #107 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031023 | 2 |
| #26022181 | 2 |
| #26021247 | 2 |
| #26018265 | 2 |
| #26018264 | 2 |
| #26018175 | 2 |
| C89×#2187 | 2 |
| #12103 | 89 |