Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
516 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 103 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. #23772038 | C2 | semidirect |
| 2. #23763477 | C2 | semidirect |
| 4. #23761253 | C2 | semidirect |
| 18. #390×C79 | C4 | semidirect |
| 19. #390×C79 | C4 | semidirect |
| 22. #384×C79 | C4 | semidirect |
| 23. #382×C79 | C4 | semidirect |
| 194. C79 | #9446 | semidirect |
| 203. #390 | Dic79 | semidirect |
| 204. #390 | Dic79 | semidirect |
| 207. #384 | Dic79 | semidirect |
| 208. #382 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772038 | 2 |
| #23763477 | 2 |
| #23761929 | 2 |
| #23761253 | 2 |
| C79×#2500 | 2 |
| #9446 | 79 |