Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
308 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 65 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. #26033208 | C2 | semidirect |
| 2. #26022493 | C2 | semidirect |
| 3. #26019733 | C2 | semidirect |
| 4. #26018303 | C2 | semidirect |
| 5. #26018233 | C2 | semidirect |
| 6. #26018219 | C2 | semidirect |
| 90. D8×C89 | SD16 | semidirect |
| 153. C89 | #12360 | semidirect |
| 221. D8 | #13083562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033208 | 2 |
| #26022493 | 2 |
| #26019733 | 2 |
| #26018303 | 2 |
| #26018233 | 2 |
| #26018219 | 2 |
| C89×#2206 | 2 |
| #12360 | 89 |