Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
468 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 83 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×#19151395 | C2 | semidirect |
| 2. C2×#19151393 | C2 | semidirect |
| 3. #26018409 | C2 | direct (N × H) |
| 8. #19151395 | C22 | semidirect |
| 10. #19151393 | C22 | semidirect |
| 13. C2×#127×C89 | C4 | semidirect |
| 17. #496×C89 | C4 | semidirect |
| 19. C2×#97×C89 | C4 | semidirect |
| 41. #127×C89 | C2×C4 | semidirect |
| 50. #97×C89 | C2×C4 | semidirect |
| 159. C2×C89 | #1406 | semidirect |
| 165. C89 | C2×#1406 | semidirect |
| 168. C2×#127 | Dic89 | semidirect |
| 172. #496 | Dic89 | semidirect |
| 176. C2×#97 | Dic89 | semidirect |
| 197. #127 | C2×Dic89 | semidirect |
| 211. #97 | C2×Dic89 | semidirect |
| 319. C2 | #26018409 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151395 | 2 |
| C2×#19151393 | 2 |
| #26018409 | 2 |
| C2×#496×C89 | 2 |
| C2×#1406 | 89 |