Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
368 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 71 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. #26022505 | C2 | semidirect |
| 3. #26022302 | C2 | semidirect |
| 5. #26018300 | C2 | semidirect |
| 7. C89×#1332 | C2 | semidirect |
| 106. D356 | Q32 | semidirect |
| 144. #1332 | D89 | semidirect |
| 146. C89 | #12322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×D356 | 2 |
| #26022505 | 2 |
| #26022302 | 2 |
| #26019618 | 2 |
| #26018300 | 2 |
| #26018208 | 2 |
| C89×#1332 | 2 |
| #12322 | 89 |