Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
820 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 131 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. #23764233 | C2 | semidirect |
| 2. #23762122 | C2 | semidirect |
| 3. #23762035 | C2 | semidirect |
| 4. #23761908 | C2 | semidirect |
| 6. #19098620 | C22 | semidirect |
| 7. #19098587 | C22 | semidirect |
| 9. #19098409 | C22 | semidirect |
| 16. #555×C79 | C4 | semidirect |
| 18. D42×C79 | C4 | semidirect |
| 160. C79 | #8491 | semidirect |
| 163. #555 | Dic79 | semidirect |
| 165. D42 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764233 | 2 |
| #23762122 | 2 |
| #23762035 | 2 |
| #23761908 | 2 |
| C79×#3549 | 2 |
| #8491 | 79 |