Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
998 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 998 conjugacy classes of subgroups — too many to draw. Only its 131 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. #26020244 | C2 | semidirect |
| 3. #26018932 | C2 | semidirect |
| 4. #26018678 | C2 | semidirect |
| 5. C89×#1460 | C2 | semidirect |
| 141. D356 | #100 | semidirect |
| 184. #1460 | D89 | semidirect |
| 185. C89 | #8393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152253 | 2 |
| #26020244 | 2 |
| #26018932 | 2 |
| #26018678 | 2 |
| C89×#1460 | 2 |
| #8393 | 89 |