Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
464 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 87 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. #23763388 | C2 | semidirect |
| 2. #23761741 | C2 | semidirect |
| 3. #23761424 | C2 | semidirect |
| 4. #23761397 | C2 | semidirect |
| 12. C2×#121×C79 | C4 | semidirect |
| 14. #400×C79 | C4 | semidirect |
| 17. #394×C79 | C4 | semidirect |
| 22. #381×C79 | C4 | semidirect |
| 209. C79 | #11824 | semidirect |
| 210. C2×#121 | Dic79 | semidirect |
| 214. #400 | Dic79 | semidirect |
| 217. #394 | Dic79 | semidirect |
| 222. #381 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763388 | 2 |
| #23761741 | 2 |
| #23761424 | 2 |
| #23761397 | 2 |
| C79×#2635 | 2 |
| #11824 | 79 |