Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
544 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26020330 | C2 | semidirect |
| 4. #26018159 | C2 | semidirect |
| 166. C89 | #9507 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029281 | 2 |
| #26024560 | 2 |
| #26020330 | 2 |
| #26018159 | 2 |
| C89×#1465 | 2 |
| #9507 | 89 |