Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
494 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 71 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. #23761737 | C2 | semidirect |
| 3. #23761717 | C2 | semidirect |
| 4. #23761334 | C2 | semidirect |
| 5. #23761331 | C2 | semidirect |
| 6. #23761331 | C2 | semidirect |
| 7. C79×#1319 | C2 | semidirect |
| 221. #1319 | D79 | semidirect |
| 224. C79 | #11566 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23768373 | 2 |
| #23761737 | 2 |
| #23761717 | 2 |
| #23761334 | 2 |
| #23761331 | 2 |
| C79×#1319 | 2 |
| #11566 | 79 |