Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
742 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 742 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. #26031005 | C2 | semidirect |
| 3. #26020164 | C2 | semidirect |
| 4. #26018616 | C2 | semidirect |
| 5. #26018613 | C2 | semidirect |
| 6. #26018128 | C2 | semidirect |
| 7. C89×#3007 | C2 | semidirect |
| 248. #3007 | D89 | semidirect |
| 254. C89 | #9975 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031005 | 2 |
| #26029504 | 2 |
| #26020164 | 2 |
| #26018616 | 2 |
| #26018613 | 2 |
| #26018128 | 2 |
| C89×#3007 | 2 |
| #9975 | 89 |