Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
460 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 69 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. #26018583 | C2 | semidirect |
| 3. #26018563 | C2 | semidirect |
| 4. #26018200 | C2 | semidirect |
| 7. C89×#1326 | C2 | semidirect |
| 212. #1326 | D89 | semidirect |
| 215. C89 | #11542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26024525 | 2 |
| #26018583 | 2 |
| #26018563 | 2 |
| #26018200 | 2 |
| #26018179 | 2 |
| C89×#1326 | 2 |
| #11542 | 89 |