Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
512 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23774054 | C2 | semidirect |
| 3. #23765619 | C2 | semidirect |
| 4. #23765575 | C2 | semidirect |
| 5. #23765480 | C2 | semidirect |
| 8. #23765294 | C2 | semidirect |
| 9. #23765290 | C2 | semidirect |
| 10. #23765213 | C2 | semidirect |
| 11. C79×#2239 | C2 | semidirect |
| 17. #19098963 | C22 | semidirect |
| 18. #19098941 | C22 | semidirect |
| 26. #19098670 | C22 | semidirect |
| 27. #19098669 | C22 | semidirect |
| 31. #19098387 | C22 | semidirect |
| 32. #19098383 | C22 | semidirect |
| 33. #19098378 | C22 | semidirect |
| 37. #19098340 | C22 | semidirect |
| 40. #365×C79 | C22 | semidirect |
| 41. #362×C79 | C22 | semidirect |
| 201. #2239 | D79 | semidirect |
| 209. C79 | #33693 | semidirect |
| 232. #365 | C2×D79 | semidirect |
| 235. #362 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774054 | 2 |
| #23772302 | 2 |
| #23765619 | 2 |
| #23765575 | 2 |
| #23765480 | 2 |
| #23765353 | 2 |
| #23765350 | 2 |
| #23765294 | 2 |
| #23765290 | 2 |
| #23765213 | 2 |
| C79×#2239 | 2 |
| #33693 | 79 |