Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
512 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23774060 | C2 | semidirect |
| 3. #23765621 | C2 | semidirect |
| 4. #23765573 | C2 | semidirect |
| 5. #23765482 | C2 | semidirect |
| 6. #23765481 | C2 | semidirect |
| 8. #23765290 | C2 | semidirect |
| 9. #23765288 | C2 | semidirect |
| 10. #23765215 | C2 | semidirect |
| 11. C79×#2231 | C2 | semidirect |
| 17. #19098943 | C22 | semidirect |
| 26. #19098669 | C22 | semidirect |
| 31. #19098385 | C22 | semidirect |
| 32. #19098384 | C22 | semidirect |
| 33. #19098380 | C22 | semidirect |
| 34. #19098378 | C22 | semidirect |
| 37. #19098340 | C22 | semidirect |
| 38. #499×C79 | C22 | semidirect |
| 40. #365×C79 | C22 | semidirect |
| 41. #364×C79 | C22 | semidirect |
| 211. #2231 | D79 | semidirect |
| 218. C79 | #33693 | semidirect |
| 224. #499 | C2×D79 | semidirect |
| 241. #365 | C2×D79 | semidirect |
| 243. #364 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774060 | 2 |
| #23772298 | 2 |
| #23765621 | 2 |
| #23765573 | 2 |
| #23765482 | 2 |
| #23765481 | 2 |
| #23765352 | 2 |
| #23765290 | 2 |
| #23765288 | 2 |
| #23765215 | 2 |
| C79×#2231 | 2 |
| #33693 | 79 |