Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
492 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26018866 | C2 | semidirect |
| 5. #26018672 | C2 | semidirect |
| 6. #26018123 | C2 | semidirect |
| 7. C89×#1302 | C2 | semidirect |
| 198. #1302 | D89 | semidirect |
| 200. C89 | #9312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030415 | 2 |
| #26028677 | 2 |
| #26018866 | 2 |
| #26018687 | 2 |
| #26018672 | 2 |
| #26018123 | 2 |
| C89×#1302 | 2 |
| #9312 | 89 |