Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
772 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 772 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 |
|---|---|---|
| 1. #23772448 | C2 | semidirect |
| 2. #23763331 | C2 | semidirect |
| 3. #23763321 | C2 | semidirect |
| 4. #23761943 | C2 | semidirect |
| 5. #23761307 | C2 | semidirect |
| 6. #23761276 | C2 | semidirect |
| 28. #450×C79 | C4 | semidirect |
| 30. #447×C79 | C4 | semidirect |
| 282. C79 | #9520 | semidirect |
| 287. #450 | Dic79 | semidirect |
| 289. #447 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772448 | 2 |
| #23763331 | 2 |
| #23763321 | 2 |
| #23761943 | 2 |
| #23761307 | 2 |
| #23761276 | 2 |
| C79×#3003 | 2 |
| #9520 | 79 |