Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
578 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 578 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 |
|---|---|---|
| 2. #26021226 | C2 | semidirect |
| 4. #26018134 | C2 | semidirect |
| 20. #497×C89 | C4 | semidirect |
| 47. C4⋊Q8×C89 | C2×C4 | semidirect |
| 55. #97×C89 | C2×C4 | semidirect |
| 167. C89 | #9003 | semidirect |
| 173. #497 | Dic89 | semidirect |
| 198. C4⋊Q8 | C2×Dic89 | semidirect |
| 214. #97 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023426 | 2 |
| #26021226 | 2 |
| C2×#19151338 | 2 |
| #26018134 | 2 |
| C2×#497×C89 | 2 |
| #9003 | 89 |