Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
772 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 772 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 |
|---|---|---|
| 2. #23772448 | C2 | semidirect |
| 3. #23763330 | C2 | semidirect |
| 4. #23763320 | C2 | semidirect |
| 5. #23761306 | C2 | semidirect |
| 6. #23761276 | C2 | semidirect |
| 7. C79×#1513 | C2 | semidirect |
| 11. #19098713 | C4 | semidirect |
| 13. #19098696 | C4 | semidirect |
| 279. #1513 | D79 | semidirect |
| 282. C79 | #9520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772626 | 2 |
| #23772448 | 2 |
| #23763330 | 2 |
| #23763320 | 2 |
| #23761306 | 2 |
| #23761276 | 2 |
| C79×#1513 | 2 |
| #9520 | 79 |