Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
438 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26029322 | C2 | semidirect |
| 3. #26018958 | C2 | semidirect |
| 4. #26018604 | C2 | semidirect |
| 5. #26018164 | C2 | semidirect |
| 6. #26018113 | C2 | semidirect |
| 7. C89×#1533 | C2 | semidirect |
| 169. #1533 | D89 | semidirect |
| 173. C89 | #9333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031239 | 2 |
| #26029322 | 2 |
| #26018958 | 2 |
| #26018604 | 2 |
| #26018164 | 2 |
| #26018113 | 2 |
| C89×#1533 | 2 |
| #9333 | 89 |