Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
778 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 87 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×#19098330 | C2 | semidirect |
| 3. #23761422 | C2 | semidirect |
| 4. #23761398 | C2 | semidirect |
| 5. C79×#1462 | C2 | semidirect |
| 6. C22×#11929624 | C4 | semidirect |
| 9. #19098475 | C4 | semidirect |
| 11. #19098472 | C4 | semidirect |
| 16. #19098426 | C4 | semidirect |
| 26. C22×Dic158 | C2×C4 | semidirect |
| 27. C22×D316 | C2×C4 | semidirect |
| 46. C79⋊#95 | C2×C4 | semidirect |
| 47. C79⋊#95 | C2×C4 | semidirect |
| 254. #1462 | D79 | semidirect |
| 257. C79 | #11753 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766719 | 2 |
| C2×#19098330 | 2 |
| #23761422 | 2 |
| #23761398 | 2 |
| C79×#1462 | 2 |
| #11753 | 79 |