Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
474 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 474 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. #26020435 | C2 | semidirect |
| 4. #26018772 | C2 | semidirect |
| 6. #26018128 | C2 | semidirect |
| 7. C89×#1901 | C2 | semidirect |
| 223. #1901 | D89 | semidirect |
| 229. C89 | #10558 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031005 | 2 |
| #26020715 | 2 |
| #26020435 | 2 |
| #26018772 | 2 |
| #26018769 | 2 |
| #26018128 | 2 |
| C89×#1901 | 2 |
| #10558 | 89 |