Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
456 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 456 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 |
|---|---|---|
| 4. #26021168 | C2 | semidirect |
| 5. #26018365 | C2 | semidirect |
| 6. #26018337 | C2 | semidirect |
| 7. C2×#362×C89 | C2 | semidirect |
| 11. #19152039 | C4 | semidirect |
| 170. C2×#362 | D89 | semidirect |
| 174. C89 | #13031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152039 | 2 |
| #26029168 | 2 |
| #26022002 | 2 |
| #26021168 | 2 |
| #26018365 | 2 |
| #26018337 | 2 |
| C2×#362×C89 | 2 |
| #13031 | 89 |