Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
408 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 119 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. #23763564 | C2 | semidirect |
| 2. #23761964 | C2 | semidirect |
| 4. #23761692 | C2 | semidirect |
| 16. #487×C79 | C4 | semidirect |
| 17. #486×C79 | C4 | semidirect |
| 135. C79 | #9758 | semidirect |
| 139. #487 | Dic79 | semidirect |
| 140. #486 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763564 | 2 |
| #23761964 | 2 |
| #23761960 | 2 |
| #23761692 | 2 |
| C79×#3131 | 2 |
| #9758 | 79 |