Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
512 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 135 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. #26021972 | C2 | semidirect |
| 4. #26018359 | C2 | semidirect |
| 17. #470×C89 | C4 | semidirect |
| 39. C2×Q16×C89 | C2×C4 | semidirect |
| 52. #106×C89 | C2×C4 | semidirect |
| 153. C89 | #13000 | semidirect |
| 160. #470 | Dic89 | semidirect |
| 173. C2×Q16 | C2×Dic89 | semidirect |
| 200. #106 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028842 | 2 |
| #26021972 | 2 |
| C2×#19151380 | 2 |
| #26018359 | 2 |
| C2×#470×C89 | 2 |
| #13000 | 89 |