Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
316 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 57 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. #26021945 | C2 | semidirect |
| 3. #26021940 | C2 | semidirect |
| 4. #26018425 | C2 | semidirect |
| 5. #26018418 | C2 | semidirect |
| 6. #26018418 | C2 | semidirect |
| 7. C89×#1413 | C2 | semidirect |
| 162. #1413 | D89 | semidirect |
| 165. C89 | #13611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031314 | 2 |
| #26021945 | 2 |
| #26021940 | 2 |
| #26018425 | 2 |
| #26018418 | 2 |
| C89×#1413 | 2 |
| #13611 | 89 |