Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
732 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26023426 | C2 | semidirect |
| 2. C2×#19151393 | C2 | semidirect |
| 4. #26018371 | C2 | semidirect |
| 19. #455×C89 | C4 | semidirect |
| 88. C2×Q8×C89 | C22⋊C4 | semidirect |
| 117. C42×C89 | C22⋊C4 | semidirect |
| 209. C89 | #13050 | semidirect |
| 214. #455 | Dic89 | semidirect |
| 278. C2×Q8 | C22⋊Dic89 | semidirect |
| 321. C42 | C22⋊Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023426 | 2 |
| C2×#19151393 | 2 |
| #26020200 | 2 |
| #26018371 | 2 |
| C2×#455×C89 | 2 |
| #13050 | 89 |