Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
904 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 904 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 |
|---|---|---|
| 3. #26018785 | C2 | semidirect |
| 4. #26018105 | C2 | semidirect |
| 14. C2×#124×C89 | C4 | semidirect |
| 17. #390×C89 | C4 | semidirect |
| 35. C22×Q8×C89 | C2×C4 | semidirect |
| 46. C2×C4⋊C4×C89 | C2×C4 | semidirect |
| 53. C2×C42×C89 | C2×C4 | semidirect |
| 205. C89 | #9459 | semidirect |
| 207. C2×#124 | Dic89 | semidirect |
| 213. #390 | Dic89 | semidirect |
| 223. C22×Q8 | C2×Dic89 | semidirect |
| 236. C2×C4⋊C4 | C2×Dic89 | semidirect |
| 248. C2×C42 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022830 | 2 |
| #26020173 | 2 |
| #26018785 | 2 |
| #26018105 | 2 |
| C89×#2435 | 2 |
| #9459 | 89 |