Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
620 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 1. #26023429 | C2 | semidirect |
| 2. #26018966 | C2 | semidirect |
| 3. #26018799 | C2 | semidirect |
| 4. #26018117 | C2 | semidirect |
| 16. #493×C89 | C4 | semidirect |
| 17. #492×C89 | C4 | semidirect |
| 36. C4⋊Q8×C89 | C2×C4 | semidirect |
| 39. #127×C89 | C2×C4 | semidirect |
| 46. C4×C8×C89 | C2×C4 | semidirect |
| 136. C89 | #9428 | semidirect |
| 141. #493 | Dic89 | semidirect |
| 142. #492 | Dic89 | semidirect |
| 159. C4⋊Q8 | C2×Dic89 | semidirect |
| 162. #127 | C2×Dic89 | semidirect |
| 174. C4×C8 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023429 | 2 |
| #26018966 | 2 |
| #26018799 | 2 |
| #26018117 | 2 |
| C89×#3151 | 2 |
| #9428 | 89 |