Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
840 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 840 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. #26022605 | C2 | semidirect |
| 2. #26018768 | C2 | semidirect |
| 3. #26018579 | C2 | semidirect |
| 4. #26018138 | C2 | semidirect |
| 17. #399×C89 | C4 | semidirect |
| 18. #392×C89 | C4 | semidirect |
| 31. #15667919 | D4 | semidirect |
| 35. C22×D4×C89 | C2×C4 | semidirect |
| 43. C2×C4⋊C4×C89 | C2×C4 | semidirect |
| 53. #95×C89 | C2×C4 | semidirect |
| 194. C89 | #9409 | semidirect |
| 201. #399 | Dic89 | semidirect |
| 202. #392 | Dic89 | semidirect |
| 213. C22×D4 | C2×Dic89 | semidirect |
| 223. C2×C4⋊C4 | C2×Dic89 | semidirect |
| 242. #95 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022605 | 2 |
| #26018768 | 2 |
| #26018579 | 2 |
| #26018138 | 2 |
| C89×#2539 | 2 |
| #9409 | 89 |