Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
698 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 91 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. #23763474 | C2 | semidirect |
| 2. C2×#19098287 | C2 | semidirect |
| 3. #23761421 | C2 | semidirect |
| 4. #23761397 | C2 | semidirect |
| 12. C22×#41×C79 | C4 | semidirect |
| 15. #393×C79 | C4 | semidirect |
| 17. #392×C79 | C4 | semidirect |
| 22. #381×C79 | C4 | semidirect |
| 240. C79 | #11839 | semidirect |
| 241. C22×#41 | Dic79 | semidirect |
| 245. #393 | Dic79 | semidirect |
| 247. #392 | Dic79 | semidirect |
| 252. #381 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763474 | 2 |
| C2×#19098287 | 2 |
| #23761421 | 2 |
| #23761397 | 2 |
| C79×#2404 | 2 |
| #11839 | 79 |