Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
390 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26029349 | C2 | semidirect |
| 3. #26018950 | C2 | semidirect |
| 6. #26018113 | C2 | semidirect |
| 7. C89×#1290 | C2 | semidirect |
| 165. #1290 | D89 | semidirect |
| 167. C89 | #9372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031452 | 2 |
| #26029349 | 2 |
| #26018950 | 2 |
| #26018886 | 2 |
| #26018650 | 2 |
| #26018113 | 2 |
| C89×#1290 | 2 |
| #9372 | 89 |