Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
970 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 970 conjugacy classes of subgroups — too many to draw. Only its 167 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. #26030382 | C2 | semidirect |
| 3. #26019242 | C2 | semidirect |
| 4. #26019208 | C2 | semidirect |
| 5. #26018763 | C2 | semidirect |
| 193. C89 | #18181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034055 | 2 |
| #26030382 | 2 |
| #26019242 | 2 |
| #26019208 | 2 |
| #26018763 | 2 |
| #26018593 | 2 |
| C89×#2398 | 2 |
| #18181 | 89 |