Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
420 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 79 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. C2×#19151395 | C2 | semidirect |
| 2. C2×#19151393 | C2 | semidirect |
| 3. #26018412 | C2 | semidirect |
| 4. #26018409 | C2 | semidirect |
| 14. #532×C89 | C4 | semidirect |
| 16. #497×C89 | C4 | semidirect |
| 18. #496×C89 | C4 | semidirect |
| 22. C4×M16×C89 | C4 | semidirect |
| 45. C4⋊Q8×C89 | C2×C4 | semidirect |
| 46. #127×C89 | C2×C4 | semidirect |
| 57. #97×C89 | C2×C4 | semidirect |
| 58. #97×C89 | C2×C4 | semidirect |
| 182. C89 | #13578 | semidirect |
| 185. #532 | Dic89 | semidirect |
| 187. #497 | Dic89 | semidirect |
| 189. #496 | Dic89 | semidirect |
| 195. C4×M16 | Dic89 | semidirect |
| 217. C4⋊Q8 | C2×Dic89 | semidirect |
| 218. #127 | C2×Dic89 | semidirect |
| 234. #97 | C2×Dic89 | semidirect |
| 235. #97 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151395 | 2 |
| C2×#19151393 | 2 |
| #26018412 | 2 |
| #26018409 | 2 |
| C89×#3153 | 2 |
| #13578 | 89 |