Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
564 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 564 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 |
|---|---|---|
| 1. #26028842 | C2 | semidirect |
| 2. #26021968 | C2 | semidirect |
| 3. C2×#19151380 | C2 | semidirect |
| 4. #26018359 | C2 | semidirect |
| 17. #469×C89 | C4 | semidirect |
| 31. #15667946 | D4 | semidirect |
| 40. C2×D8×C89 | C2×C4 | semidirect |
| 52. #106×C89 | C2×C4 | semidirect |
| 162. C89 | #12999 | semidirect |
| 169. #469 | Dic89 | semidirect |
| 183. C2×D8 | C2×Dic89 | semidirect |
| 209. #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 |
| #26021968 | 2 |
| C2×#19151380 | 2 |
| #26018359 | 2 |
| C2×#469×C89 | 2 |
| #12999 | 89 |