Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
382 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 22. #500×C79 | C4 | semidirect |
| 23. #498×C79 | C4 | semidirect |
| 24. #487×C79 | C4 | semidirect |
| 25. #487×C79 | C4 | semidirect |
| 165. C79 | #9280 | semidirect |
| 168. #500 | Dic79 | semidirect |
| 169. #498 | Dic79 | semidirect |
| 170. #487 | Dic79 | semidirect |
| 171. #487 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772495 | 2 |
| #23761912 | 2 |
| #23761873 | 2 |
| #23761262 | 2 |
| #23761228 | 2 |
| C79×#3231 | 2 |
| #9280 | 79 |