Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
768 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 768 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 |
|---|---|---|
| 1. #26031000 | C2 | semidirect |
| 2. #26029504 | C2 | semidirect |
| 3. #26020164 | C2 | semidirect |
| 4. #26018613 | C2 | semidirect |
| 5. #26018612 | C2 | semidirect |
| 6. #26018128 | C2 | semidirect |
| 7. C89×#3006 | C2 | semidirect |
| 258. #3006 | D89 | semidirect |
| 263. C89 | #9974 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031000 | 2 |
| #26029504 | 2 |
| #26020164 | 2 |
| #26018613 | 2 |
| #26018612 | 2 |
| #26018128 | 2 |
| C89×#3006 | 2 |
| #9974 | 89 |