Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
380 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 55 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. #23771201 | C2 | semidirect |
| 4. #23761430 | C2 | semidirect |
| 5. #23761407 | C2 | semidirect |
| 6. #23761345 | C2 | semidirect |
| 185. C79 | #12146 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771201 | 2 |
| #23764621 | 2 |
| #23762403 | 2 |
| #23761430 | 2 |
| #23761407 | 2 |
| #23761345 | 2 |
| C79×#1604 | 2 |
| #12146 | 79 |