Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
476 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 476 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. #23762038 | C2 | semidirect |
| 4. #23761873 | C2 | semidirect |
| 6. #23761263 | C2 | semidirect |
| 7. C79×#3237 | C2 | semidirect |
| 188. #3237 | D79 | semidirect |
| 195. C79 | #10043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773495 | 2 |
| #23773404 | 2 |
| #23762038 | 2 |
| #23761873 | 2 |
| #23761740 | 2 |
| #23761263 | 2 |
| C79×#3237 | 2 |
| #10043 | 79 |