Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
540 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 95 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. #26029323 | C2 | semidirect |
| 3. #26018965 | C2 | semidirect |
| 4. #26018125 | C2 | semidirect |
| 5. C89×#1536 | C2 | semidirect |
| 126. #1536 | D89 | semidirect |
| 128. C89 | #9423 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030705 | 2 |
| #26029323 | 2 |
| #26018965 | 2 |
| #26018125 | 2 |
| C89×#1536 | 2 |
| #9423 | 89 |