Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
306 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 2. #26022455 | C2 | semidirect |
| 3. #26022450 | C2 | semidirect |
| 5. #26018271 | C2 | semidirect |
| 6. #26018271 | C2 | semidirect |
| 158. C89 | #12286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031147 | 2 |
| #26022455 | 2 |
| #26022450 | 2 |
| #26021692 | 2 |
| #26018271 | 2 |
| C89×#1315 | 2 |
| #12286 | 89 |