Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
454 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 3. #23761873 | C2 | semidirect |
| 5. #23761756 | C2 | semidirect |
| 6. #23761272 | C2 | semidirect |
| 7. C79×#3166 | C2 | semidirect |
| 184. #3166 | D79 | semidirect |
| 189. C79 | #10126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774590 | 2 |
| #23774407 | 2 |
| #23761873 | 2 |
| #23761818 | 2 |
| #23761756 | 2 |
| #23761272 | 2 |
| C79×#3166 | 2 |
| #10126 | 79 |