Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
504 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 97 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. #23762085 | C2 | semidirect |
| 5. #23761291 | C2 | semidirect |
| 6. #23761289 | C2 | semidirect |
| 7. C79×#1549 | C2 | semidirect |
| 178. #1549 | D79 | semidirect |
| 181. C79 | #9435 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773857 | 2 |
| #23772466 | 2 |
| #23762133 | 2 |
| #23762085 | 2 |
| #23761291 | 2 |
| #23761289 | 2 |
| C79×#1549 | 2 |
| #9435 | 79 |