Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1092 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 1092 conjugacy classes of subgroups — too many to draw. Only its 119 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. #26021093 | C2 | semidirect |
| 3. #26018985 | C2 | semidirect |
| 4. #26018843 | C2 | semidirect |
| 5. #26018692 | C2 | semidirect |
| 6. #26018689 | C2 | semidirect |
| 7. C89×#1965 | C2 | semidirect |
| 21. #19151622 | C22 | semidirect |
| 23. C4×#13083558 | C22 | semidirect |
| 32. #423×C89 | C22 | semidirect |
| 34. C4×M16×C89 | C22 | semidirect |
| 226. D356 | #100 | semidirect |
| 236. Dic178 | #100 | semidirect |
| 279. #1965 | D89 | semidirect |
| 284. C89 | #8469 | semidirect |
| 300. #423 | C2×D89 | semidirect |
| 304. C4×M16 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034028 | 2 |
| #26021093 | 2 |
| #26018985 | 2 |
| #26018843 | 2 |
| #26018692 | 2 |
| #26018689 | 2 |
| C89×#1965 | 2 |
| #8469 | 89 |