Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
436 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #23772505 | C2 | semidirect |
| 5. #23762037 | C2 | semidirect |
| 6. #23761272 | C2 | semidirect |
| 7. C79×#1291 | C2 | semidirect |
| 151. #1291 | D79 | semidirect |
| 152. C79 | #9424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773775 | 2 |
| #23772505 | 2 |
| #23762113 | 2 |
| #23762037 | 2 |
| #23761272 | 2 |
| C79×#1291 | 2 |
| #9424 | 79 |