Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
568 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23763133 | C2 | semidirect |
| 2. #23761714 | C2 | semidirect |
| 3. #23761397 | C2 | semidirect |
| 11. C2×#127×C79 | C4 | semidirect |
| 15. #394×C79 | C4 | semidirect |
| 19. #382×C79 | C4 | semidirect |
| 182. C79 | #11693 | semidirect |
| 183. C2×#127 | Dic79 | semidirect |
| 189. #394 | Dic79 | semidirect |
| 193. #382 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763133 | 2 |
| #23761714 | 2 |
| #23761397 | 2 |
| C79×#2619 | 2 |
| #11693 | 79 |