Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
324 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 53 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. #26022472 | C2 | semidirect |
| 3. #26022469 | C2 | semidirect |
| 5. #26018245 | C2 | semidirect |
| 7. C89×#1342 | C2 | semidirect |
| 156. #1342 | D89 | semidirect |
| 158. C89 | #12299 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031072 | 2 |
| #26022472 | 2 |
| #26022469 | 2 |
| #26021769 | 2 |
| #26018245 | 2 |
| #26018187 | 2 |
| C89×#1342 | 2 |
| #12299 | 89 |