Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
456 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 3. #26018264 | C2 | semidirect |
| 11. C22×Q16×C89 | C4 | semidirect |
| 16. #467×C89 | C4 | semidirect |
| 18. C2×#107×C89 | C4 | semidirect |
| 152. C89 | #11706 | semidirect |
| 153. C22×Q16 | Dic89 | semidirect |
| 160. #467 | Dic89 | semidirect |
| 162. C2×#107 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021863 | 2 |
| #26019969 | 2 |
| #26018264 | 2 |
| C2×#467×C89 | 2 |
| #11706 | 89 |