Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
820 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 820 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 |
|---|---|---|
| 2. #23764231 | C2 | semidirect |
| 3. #23762120 | C2 | semidirect |
| 4. #23762034 | C2 | semidirect |
| 5. #23761909 | C2 | semidirect |
| 6. #23761908 | C2 | semidirect |
| 7. C79×#1557 | C2 | semidirect |
| 11. #19099278 | C4 | semidirect |
| 13. D4×D316 | C4 | semidirect |
| 20. #19098620 | C22 | semidirect |
| 22. #19098409 | C22 | semidirect |
| 29. #432×C79 | C22 | semidirect |
| 30. #423×C79 | C22 | semidirect |
| 237. #1557 | D79 | semidirect |
| 241. C79 | #8491 | semidirect |
| 256. #432 | C2×D79 | semidirect |
| 257. #423 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777805 | 2 |
| #23764231 | 2 |
| #23762120 | 2 |
| #23762034 | 2 |
| #23761909 | 2 |
| #23761908 | 2 |
| C79×#1557 | 2 |
| #8491 | 79 |