Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
2062 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 2062 conjugacy classes of subgroups — too many to draw. Only its 331 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. C22×#15667927 | C2 | semidirect |
| 2. C2×#19151391 | C2 | direct (N × H) |
| 6. C2×#15667927 | C22 | semidirect |
| 7. #19151391 | C22 | direct (N × H) |
| 9. C23×D4×C89 | C4 | semidirect |
| 12. C2×#127×C89 | C4 | semidirect |
| 14. C22×C42×C89 | C4 | semidirect |
| 19. #15667927 | C23 | semidirect |
| 31. C22×D4×C89 | C2×C4 | semidirect |
| 38. #127×C89 | C2×C4 | semidirect |
| 41. C2×C42×C89 | C2×C4 | semidirect |
| 73. C2×D4×C89 | C22×C4 | semidirect |
| 83. C42×C89 | C22×C4 | semidirect |
| 136. C22×C89 | #353 | semidirect |
| 150. C2×C89 | C2×#353 | semidirect |
| 155. C89 | C22×#353 | semidirect |
| 157. C23×D4 | Dic89 | semidirect |
| 160. C2×#127 | Dic89 | semidirect |
| 163. C22×C42 | Dic89 | semidirect |
| 178. C22×D4 | C2×Dic89 | semidirect |
| 186. #127 | C2×Dic89 | semidirect |
| 191. C2×C42 | C2×Dic89 | semidirect |
| 221. C2×D4 | C22×Dic89 | semidirect |
| 235. C42 | C22×Dic89 | semidirect |
| 288. C22 | #19151391 | direct (N × H) |
| 301. C2 | C2×#19151391 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667927 | 2 |
| C2×#19151391 | 2 |
| C22×#127×C89 | 2 |
| C22×#353 | 89 |