Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
452 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #26018283 | C2 | semidirect |
| 5. #26018281 | C2 | semidirect |
| 6. #26018279 | C2 | semidirect |
| 7. C89×#1353 | C2 | semidirect |
| 195. #1353 | D89 | semidirect |
| 196. C89 | #11722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026066 | 2 |
| #343×D89 | 2 |
| #324×D89 | 2 |
| #26018283 | 2 |
| #26018281 | 2 |
| #26018279 | 2 |
| C89×#1353 | 2 |
| #11722 | 89 |