Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
498 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 1. #23772539 | C2 | semidirect |
| 2. #23764328 | C2 | semidirect |
| 3. #23762114 | C2 | semidirect |
| 4. #23761925 | C2 | semidirect |
| 5. #23761269 | C2 | semidirect |
| 6. #23761255 | C2 | semidirect |
| 26. #496×C79 | C4 | semidirect |
| 27. #490×C79 | C4 | semidirect |
| 223. C79 | #9378 | semidirect |
| 226. #496 | Dic79 | semidirect |
| 227. #490 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772539 | 2 |
| #23764328 | 2 |
| #23762114 | 2 |
| #23761925 | 2 |
| #23761269 | 2 |
| #23761255 | 2 |
| C79×#3217 | 2 |
| #9378 | 79 |