Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
396 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 61 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. #26031605 | C2 | semidirect |
| 2. #26022180 | C2 | semidirect |
| 4. #26021564 | C2 | semidirect |
| 5. #26018260 | C2 | semidirect |
| 6. #26018191 | C2 | semidirect |
| 7. C89×#1348 | C2 | semidirect |
| 185. #1348 | D89 | semidirect |
| 188. C89 | #12160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031605 | 2 |
| #26022180 | 2 |
| #26022166 | 2 |
| #26021564 | 2 |
| #26018260 | 2 |
| #26018191 | 2 |
| C89×#1348 | 2 |
| #12160 | 89 |