Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
462 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26019938 | C2 | semidirect |
| 2. #26019015 | C2 | semidirect |
| 3. #26018863 | C2 | semidirect |
| 4. #26018760 | C2 | semidirect |
| 16. #500×C89 | C4 | semidirect |
| 17. #493×C89 | C4 | semidirect |
| 18. #486×C89 | C4 | semidirect |
| 145. C89 | #9762 | semidirect |
| 147. #500 | Dic89 | semidirect |
| 148. #493 | Dic89 | semidirect |
| 149. #486 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26019938 | 2 |
| #26019015 | 2 |
| #26018863 | 2 |
| #26018760 | 2 |
| C89×#3169 | 2 |
| #9762 | 89 |