Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
764 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 81 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. #23771427 | C2 | semidirect |
| 3. #23763318 | C2 | semidirect |
| 4. #23761933 | C2 | semidirect |
| 5. #23761930 | C2 | semidirect |
| 6. #23761309 | C2 | semidirect |
| 7. C79×#3007 | C2 | semidirect |
| 256. #3007 | D79 | semidirect |
| 263. C79 | #9981 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772652 | 2 |
| #23771427 | 2 |
| #23763318 | 2 |
| #23761933 | 2 |
| #23761930 | 2 |
| #23761309 | 2 |
| C79×#3007 | 2 |
| #9981 | 79 |