Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
444 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 4. #23761334 | C2 | semidirect |
| 5. #23761333 | C2 | semidirect |
| 6. #23761333 | C2 | semidirect |
| 7. C79×#1319 | C2 | semidirect |
| 204. #1319 | D79 | semidirect |
| 205. C79 | #11564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23768397 | 2 |
| #23761737 | 2 |
| #23761717 | 2 |
| #23761334 | 2 |
| #23761333 | 2 |
| C79×#1319 | 2 |
| #11564 | 79 |