Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
434 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 434 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 |
| 13. C2×#117×C79 | C4 | semidirect |
| 14. #400×C79 | C4 | semidirect |
| 16. #398×C79 | C4 | semidirect |
| 22. C4×C22⋊C4×C79 | C4 | semidirect |
| 188. C79 | #11822 | semidirect |
| 190. C2×#117 | Dic79 | semidirect |
| 193. #400 | Dic79 | semidirect |
| 195. #398 | Dic79 | semidirect |
| 202. C4×C22⋊C4 | 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 |
| #23761400 | 2 |
| C79×#2395 | 2 |
| #11822 | 79 |