Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
408 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23763564 | C2 | semidirect |
| 3. #23761965 | C2 | semidirect |
| 5. C79×#1452 | C2 | semidirect |
| 9. #19098914 | C4 | semidirect |
| 10. #19098910 | C4 | semidirect |
| 134. #1452 | D79 | semidirect |
| 135. C79 | #9758 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773723 | 2 |
| #23763564 | 2 |
| #23761965 | 2 |
| #23761961 | 2 |
| C79×#1452 | 2 |
| #9758 | 79 |