Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1000 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 1000 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. #26021898 | C2 | semidirect |
| 2. #26020180 | C2 | semidirect |
| 3. #26020170 | C2 | semidirect |
| 6. C2×#15667929 | C22 | semidirect |
| 8. C2×#15667927 | C22 | semidirect |
| 13. C2×H(5,𝔽2)×C89 | C4 | semidirect |
| 22. C2×#123×C89 | C4 | semidirect |
| 23. #518×C89 | C4 | semidirect |
| 237. C89 | #12706 | semidirect |
| 238. C2×H(5,𝔽2) | Dic89 | semidirect |
| 247. C2×#123 | Dic89 | semidirect |
| 248. #518 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021898 | 2 |
| #26020180 | 2 |
| #26020170 | 2 |
| C89×#3485 | 2 |
| #12706 | 89 |