Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
786 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 119 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. #26018095 | C2 | semidirect |
| 4. #26018094 | C2 | semidirect |
| 5. C89×#1280 | C2 | semidirect |
| 174. #1280 | D89 | semidirect |
| 175. C89 | #8702 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151460 | 2 |
| #26020161 | 2 |
| #26018095 | 2 |
| #26018094 | 2 |
| C89×#1280 | 2 |
| #8702 | 89 |