Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
342 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 59 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. #26022188 | C2 | semidirect |
| 4. #26021520 | C2 | semidirect |
| 5. #26018271 | C2 | semidirect |
| 7. C89×#1323 | C2 | semidirect |
| 166. #1323 | D89 | semidirect |
| 167. C89 | #12169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031713 | 2 |
| #26022188 | 2 |
| #26022171 | 2 |
| #26021520 | 2 |
| #26018271 | 2 |
| #26018268 | 2 |
| C89×#1323 | 2 |
| #12169 | 89 |