Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
632 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26023431 | C2 | semidirect |
| 3. C2×#19151396 | C2 | semidirect |
| 5. #26018379 | C2 | semidirect |
| 6. #26018378 | C2 | semidirect |
| 11. #19151781 | C4 | semidirect |
| 252. C89 | #13056 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151781 | 2 |
| #26023431 | 2 |
| C2×#19151396 | 2 |
| #26020211 | 2 |
| #26018379 | 2 |
| #26018378 | 2 |
| C89×#1793 | 2 |
| #13056 | 89 |