Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
180 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 180 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 |
|---|---|---|
| 1. #26022529 | C2 | semidirect |
| 3. #26018433 | C2 | semidirect |
| 6. C32×Dic89 | C2 | semidirect |
| 7. C89×#1416 | C2 | semidirect |
| 89. #1416 | D89 | semidirect |
| 93. C89 | #13721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022529 | 2 |
| #26022514 | 2 |
| #26018433 | 2 |
| #26018431 | 2 |
| #26018429 | 2 |
| C32×Dic89 | 2 |
| C89×#1416 | 2 |
| #13721 | 89 |