Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
380 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 20. #498×C79 | C4 | semidirect |
| 21. #494×C79 | C4 | semidirect |
| 22. #487×C79 | C4 | semidirect |
| 23. #487×C79 | C4 | semidirect |
| 155. C79 | #9416 | semidirect |
| 158. #498 | Dic79 | semidirect |
| 159. #494 | Dic79 | semidirect |
| 160. #487 | Dic79 | semidirect |
| 161. #487 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772506 | 2 |
| #23762038 | 2 |
| #23761951 | 2 |
| #23761272 | 2 |
| #23761265 | 2 |
| C79×#3185 | 2 |
| #9416 | 79 |