Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
392 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 3. #26019035 | C2 | semidirect |
| 4. #26018751 | C2 | semidirect |
| 6. #26018107 | C2 | semidirect |
| 7. C89×#1552 | C2 | semidirect |
| 187. #1552 | D89 | semidirect |
| 191. C89 | #10510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031251 | 2 |
| #26021182 | 2 |
| #26019035 | 2 |
| #26018751 | 2 |
| #26018605 | 2 |
| #26018107 | 2 |
| C89×#1552 | 2 |
| #10510 | 89 |