Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
694 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 694 conjugacy classes of subgroups — too many to draw. Only its 127 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. #23765095 | C2 | semidirect |
| 2. #23765075 | C2 | semidirect |
| 4. #23763504 | C2 | semidirect |
| 19. #533×C79 | C4 | semidirect |
| 21. C2×#124×C79 | C4 | semidirect |
| 22. #519×C79 | C4 | semidirect |
| 23. #518×C79 | C4 | semidirect |
| 185. C79 | #12721 | semidirect |
| 192. #533 | Dic79 | semidirect |
| 194. C2×#124 | Dic79 | semidirect |
| 195. #519 | Dic79 | semidirect |
| 196. #518 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765095 | 2 |
| #23765075 | 2 |
| #23765050 | 2 |
| #23763504 | 2 |
| C79×#3510 | 2 |
| #12721 | 79 |