Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1164 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 1164 conjugacy classes of subgroups — too many to draw. Only its 131 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. #26018249 | C2 | direct (N × H) |
| 8. #19151365 | C22 | semidirect |
| 10. #19151322 | C22 | semidirect |
| 12. C23×D4×C89 | C4 | semidirect |
| 17. #392×C89 | C4 | semidirect |
| 19. C2×#95×C89 | C4 | semidirect |
| 40. C22×D4×C89 | C2×C4 | semidirect |
| 54. #95×C89 | C2×C4 | semidirect |
| 244. C2×C89 | #1343 | semidirect |
| 252. C89 | C2×#1343 | semidirect |
| 254. C23×D4 | Dic89 | semidirect |
| 261. #392 | Dic89 | semidirect |
| 263. C2×#95 | Dic89 | semidirect |
| 280. C22×D4 | C2×Dic89 | semidirect |
| 302. #95 | C2×Dic89 | semidirect |
| 491. C2 | #26018249 | direct (N × H) |
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 |
| #26018249 | 2 |
| C2×#392×C89 | 2 |
| C2×#1343 | 89 |