Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
414 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 97 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. C4⋊C16×D89 | C2 | semidirect |
| 3. #26018999 | C2 | semidirect |
| 4. #26018302 | C2 | semidirect |
| 5. #26018300 | C2 | semidirect |
| 6. #26018298 | C2 | semidirect |
| 7. C89×#1361 | C2 | semidirect |
| 152. #1361 | D89 | semidirect |
| 153. C89 | #11929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030679 | 2 |
| C4⋊C16×D89 | 2 |
| #26018999 | 2 |
| #26018302 | 2 |
| #26018300 | 2 |
| #26018298 | 2 |
| C89×#1361 | 2 |
| #11929 | 89 |