Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
954 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 179 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 |
|---|---|---|
| 1. #23774783 | C2 | semidirect |
| 3. #23762540 | C2 | semidirect |
| 4. #23762521 | C2 | semidirect |
| 5. #23762478 | C2 | semidirect |
| 6. #23762459 | C2 | semidirect |
| 7. #23762135 | C2 | semidirect |
| 8. #23761855 | C2 | semidirect |
| 9. C79×#3550 | C2 | semidirect |
| 191. #3550 | D79 | semidirect |
| 200. C79 | #18688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774783 | 2 |
| #23773826 | 2 |
| #23762540 | 2 |
| #23762521 | 2 |
| #23762478 | 2 |
| #23762459 | 2 |
| #23762135 | 2 |
| #23761855 | 2 |
| C79×#3550 | 2 |
| #18688 | 79 |