Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1090 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1090 conjugacy classes of subgroups — too many to draw. Only its 183 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. C2×#19099006 | C2 | semidirect |
| 3. #23773055 | C2 | semidirect |
| 4. #23765353 | C2 | semidirect |
| 5. #23765137 | C2 | semidirect |
| 6. C79×#2115 | C2 | semidirect |
| 15. C22×Dic316 | C22 | semidirect |
| 18. #19099006 | C22 | semidirect |
| 21. #19098821 | C22 | semidirect |
| 23. #19098601 | C22 | semidirect |
| 25. #19098374 | C22 | semidirect |
| 27. C2×M32×C79 | C22 | semidirect |
| 28. #349×C79 | C22 | semidirect |
| 203. #2115 | D79 | semidirect |
| 204. C79 | #33532 | semidirect |
| 220. C2×M32 | C2×D79 | semidirect |
| 226. #349 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23778174 | 2 |
| C2×#19099006 | 2 |
| #23773055 | 2 |
| #23765353 | 2 |
| #23765137 | 2 |
| C79×#2115 | 2 |
| #33532 | 79 |