Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
336 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26033342 | C2 | semidirect |
| 2. #26022516 | C2 | semidirect |
| 3. #26022284 | C2 | semidirect |
| 4. #26018294 | C2 | semidirect |
| 5. #26018234 | C2 | semidirect |
| 6. #26018218 | C2 | semidirect |
| 7. C89×#1688 | C2 | semidirect |
| 165. #1688 | D89 | semidirect |
| 169. C89 | #12336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033342 | 2 |
| #26022516 | 2 |
| #26022284 | 2 |
| #26018294 | 2 |
| #26018234 | 2 |
| #26018218 | 2 |
| C89×#1688 | 2 |
| #12336 | 89 |