Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
670 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 670 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. C2×#19151365 | C2 | semidirect |
| 2. C2×#19151322 | C2 | semidirect |
| 3. #26018252 | C2 | semidirect |
| 4. #26018249 | C2 | semidirect |
| 12. C2×#121×C89 | C4 | semidirect |
| 15. #397×C89 | C4 | semidirect |
| 19. #392×C89 | C4 | semidirect |
| 22. #380×C89 | C4 | semidirect |
| 35. C22×D4×C89 | C2×C4 | semidirect |
| 43. C2×C4⋊C4×C89 | C2×C4 | semidirect |
| 58. #95×C89 | C2×C4 | semidirect |
| 59. #95×C89 | C2×C4 | semidirect |
| 248. C89 | #11692 | semidirect |
| 249. C2×#121 | Dic89 | semidirect |
| 254. #397 | Dic89 | semidirect |
| 258. #392 | Dic89 | semidirect |
| 261. #380 | Dic89 | semidirect |
| 270. C22×D4 | C2×Dic89 | semidirect |
| 280. C2×C4⋊C4 | C2×Dic89 | semidirect |
| 301. #95 | C2×Dic89 | semidirect |
| 302. #95 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151365 | 2 |
| C2×#19151322 | 2 |
| #26018252 | 2 |
| #26018249 | 2 |
| C89×#2617 | 2 |
| #11692 | 89 |