Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
426 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26018201 | C2 | semidirect |
| 4. #26018199 | C2 | semidirect |
| 181. C89 | #11578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025595 | 2 |
| #26018593 | 2 |
| #26018201 | 2 |
| #26018199 | 2 |
| C89×#1459 | 2 |
| #11578 | 89 |