Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
556 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 139 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. #26021830 | C2 | semidirect |
| 2. #26021426 | C2 | semidirect |
| 3. #26021422 | C2 | semidirect |
| 4. #26021227 | C2 | semidirect |
| 7. #26020492 | C2 | semidirect |
| 8. #26020490 | C2 | semidirect |
| 56. C4⋊Q8×C89 | Q8 | semidirect |
| 57. #127×C89 | Q8 | semidirect |
| 58. #124×C89 | Q8 | semidirect |
| 59. #124×C89 | Q8 | semidirect |
| 180. C89 | #32704 | semidirect |
| 212. C4⋊Q8 | Dic178 | semidirect |
| 213. #127 | Dic178 | semidirect |
| 215. #124 | Dic178 | semidirect |
| 216. #124 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021830 | 2 |
| #26021426 | 2 |
| #26021422 | 2 |
| #26021227 | 2 |
| #26021081 | 2 |
| #26020636 | 2 |
| #26020492 | 2 |
| #26020490 | 2 |
| C89×#1884 | 2 |
| #32704 | 89 |