Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
600 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26018696 | C2 | semidirect |
| 3. #26018586 | C2 | semidirect |
| 4. #26018117 | C2 | semidirect |
| 5. C89×#2873 | C2 | semidirect |
| 63. C4×C8×C89 | D4 | semidirect |
| 190. #2873 | D89 | semidirect |
| 195. C89 | #9492 | semidirect |
| 247. C4×C8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025818 | 2 |
| #26018696 | 2 |
| #26018586 | 2 |
| #26018117 | 2 |
| C89×#2873 | 2 |
| #9492 | 89 |