Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
506 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 506 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 |
|---|---|---|
| 3. #23761424 | C2 | semidirect |
| 4. #23761400 | C2 | semidirect |
| 12. C2×#117×C79 | C4 | semidirect |
| 14. #399×C79 | C4 | semidirect |
| 16. #397×C79 | C4 | semidirect |
| 21. #381×C79 | C4 | semidirect |
| 204. C79 | #11841 | semidirect |
| 205. C2×#117 | Dic79 | semidirect |
| 208. #399 | Dic79 | semidirect |
| 210. #397 | Dic79 | semidirect |
| 215. #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 |
| #23761424 | 2 |
| #23761400 | 2 |
| C79×#2482 | 2 |
| #11841 | 79 |