Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
272 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23765174 | C2 | semidirect |
| 4. #23761513 | C2 | semidirect |
| 5. #23761497 | C2 | semidirect |
| 6. #23761493 | C2 | semidirect |
| 138. C79 | #13503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765174 | 2 |
| C2×#19098347 | 2 |
| #23763454 | 2 |
| #23761513 | 2 |
| #23761497 | 2 |
| #23761493 | 2 |
| C79×#1813 | 2 |
| #13503 | 79 |