Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
556 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 143 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. #26021827 | C2 | semidirect |
| 2. #26021424 | C2 | semidirect |
| 3. #26021229 | C2 | semidirect |
| 5. #26020494 | C2 | semidirect |
| 35. C4⋊Q8×C89 | Q8 | semidirect |
| 36. #127×C89 | Q8 | semidirect |
| 37. #124×C89 | Q8 | semidirect |
| 126. C89 | #32704 | semidirect |
| 147. C4⋊Q8 | Dic178 | semidirect |
| 148. #127 | Dic178 | semidirect |
| 150. #124 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021827 | 2 |
| #26021424 | 2 |
| #26021229 | 2 |
| #26020636 | 2 |
| #26020494 | 2 |
| C89×#1962 | 2 |
| #32704 | 89 |