Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
314 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #26020415 | C2 | semidirect |
| 4. #26018361 | C2 | semidirect |
| 5. #26018360 | C2 | semidirect |
| 6. #26018333 | C2 | semidirect |
| 153. C89 | #13485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021964 | 2 |
| #26021141 | 2 |
| #26020415 | 2 |
| #26018361 | 2 |
| #26018360 | 2 |
| #26018333 | 2 |
| C89×#2139 | 2 |
| #13485 | 89 |