Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1122 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1122 conjugacy classes of subgroups — too many to draw. Only its 183 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. #23778174 | C2 | semidirect |
| 2. C2×#19098999 | C2 | semidirect |
| 3. #23765345 | C2 | semidirect |
| 4. #23765135 | C2 | semidirect |
| 5. #23765021 | C2 | semidirect |
| 6. C79×#3058 | C2 | semidirect |
| 12. #19099363 | C22 | semidirect |
| 16. #19098999 | C22 | semidirect |
| 19. C2×#14579101 | C22 | semidirect |
| 20. #19098372 | C22 | semidirect |
| 21. #19098345 | C22 | semidirect |
| 22. C22×D8×C79 | C22 | semidirect |
| 25. #469×C79 | C22 | semidirect |
| 27. #427×C79 | C22 | semidirect |
| 46. #14579183 | D4 | semidirect |
| 49. C2×Dic316 | D4 | semidirect |
| 53. C2×D632 | D4 | semidirect |
| 205. #3058 | D79 | semidirect |
| 209. C79 | #33531 | semidirect |
| 218. C22×D8 | C2×D79 | semidirect |
| 226. #469 | C2×D79 | semidirect |
| 228. #427 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23778174 | 2 |
| C2×#19098999 | 2 |
| #23765345 | 2 |
| #23765135 | 2 |
| #23765021 | 2 |
| C79×#3058 | 2 |
| #33531 | 79 |