Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
756 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 215 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. #26020741 | C2 | semidirect |
| 2. #26020734 | C2 | semidirect |
| 3. #26020651 | C2 | semidirect |
| 4. #26020636 | C2 | semidirect |
| 5. #26020401 | C2 | semidirect |
| 20. #496×C89 | C4 | semidirect |
| 21. #493×C89 | C4 | semidirect |
| 22. #492×C89 | C4 | semidirect |
| 39. C2×SD16×C89 | C2×C4 | semidirect |
| 40. C2×D8×C89 | C2×C4 | semidirect |
| 42. C4⋊Q8×C89 | C2×C4 | semidirect |
| 46. #127×C89 | C2×C4 | semidirect |
| 47. #124×C89 | C2×C4 | semidirect |
| 51. #97×C89 | C2×C4 | semidirect |
| 52. C4×C8×C89 | C2×C4 | semidirect |
| 143. C89 | #23361 | semidirect |
| 149. #496 | Dic89 | semidirect |
| 150. #493 | Dic89 | semidirect |
| 151. #492 | Dic89 | semidirect |
| 166. C2×SD16 | C2×Dic89 | semidirect |
| 167. C2×D8 | C2×Dic89 | semidirect |
| 172. C4⋊Q8 | C2×Dic89 | semidirect |
| 176. #127 | C2×Dic89 | semidirect |
| 177. #124 | C2×Dic89 | semidirect |
| 188. #97 | C2×Dic89 | semidirect |
| 189. C4×C8 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020741 | 2 |
| #26020734 | 2 |
| #26020651 | 2 |
| #26020636 | 2 |
| #26020401 | 2 |
| C89×#3151 | 2 |
| #23361 | 89 |