Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
520 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 520 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. #23774143 | C2 | semidirect |
| 3. #23765618 | C2 | semidirect |
| 4. #23765572 | C2 | semidirect |
| 5. #23765571 | C2 | semidirect |
| 6. #23765478 | C2 | semidirect |
| 8. #23765294 | C2 | semidirect |
| 9. #23765292 | C2 | semidirect |
| 10. #23765211 | C2 | semidirect |
| 11. C79×#2214 | C2 | semidirect |
| 16. #19098961 | C22 | semidirect |
| 26. #19098670 | C22 | semidirect |
| 30. #19098387 | C22 | semidirect |
| 31. #19098386 | C22 | semidirect |
| 32. #19098384 | C22 | semidirect |
| 33. #19098379 | C22 | semidirect |
| 37. #19098340 | C22 | semidirect |
| 39. #494×C79 | C22 | semidirect |
| 41. #364×C79 | C22 | semidirect |
| 42. #362×C79 | C22 | semidirect |
| 219. #2214 | D79 | semidirect |
| 224. C79 | #33689 | semidirect |
| 231. #494 | C2×D79 | semidirect |
| 249. #364 | C2×D79 | semidirect |
| 251. #362 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774143 | 2 |
| #23772305 | 2 |
| #23765618 | 2 |
| #23765572 | 2 |
| #23765571 | 2 |
| #23765478 | 2 |
| #23765349 | 2 |
| #23765294 | 2 |
| #23765292 | 2 |
| #23765211 | 2 |
| C79×#2214 | 2 |
| #33689 | 79 |