Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
444 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 10. #19098848 | C4 | semidirect |
| 11. #19098773 | C4 | semidirect |
| 177. C79 | #9328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773530 | 2 |
| #23766051 | 2 |
| #23764344 | 2 |
| #23761913 | 2 |
| #23761294 | 2 |
| #23761255 | 2 |
| C79×#1491 | 2 |
| #9328 | 79 |