Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
508 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 508 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. #26021179 | C2 | semidirect |
| 3. #26021170 | C2 | semidirect |
| 4. #26021091 | C2 | semidirect |
| 5. #26019005 | C2 | semidirect |
| 6. #26018930 | C2 | semidirect |
| 7. C89×#1303 | C2 | semidirect |
| 100. #13083558 | D8 | semidirect |
| 214. #1303 | D89 | semidirect |
| 215. C89 | #10500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031172 | 2 |
| #26021179 | 2 |
| #26021170 | 2 |
| #26021091 | 2 |
| #26019005 | 2 |
| #26018930 | 2 |
| C89×#1303 | 2 |
| #10500 | 89 |