Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
368 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 368 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 |
|---|---|---|
| 2. #26021871 | C2 | semidirect |
| 3. #26018204 | C2 | semidirect |
| 4. #26018188 | C2 | semidirect |
| 5. C89×#1320 | C2 | semidirect |
| 134. #1320 | D89 | semidirect |
| 135. C89 | #11484 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028951 | 2 |
| #26021871 | 2 |
| #26018204 | 2 |
| #26018188 | 2 |
| C89×#1320 | 2 |
| #11484 | 89 |