Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
568 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 91 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. #23772428 | C2 | semidirect |
| 3. #23762023 | C2 | semidirect |
| 4. #23762023 | C2 | semidirect |
| 5. #23761740 | C2 | semidirect |
| 6. #23761256 | C2 | semidirect |
| 7. C79×#1285 | C2 | semidirect |
| 66. #14579072 | D4 | semidirect |
| 78. #97×C79 | D4 | semidirect |
| 247. #1285 | D79 | semidirect |
| 248. C79 | #9447 | semidirect |
| 317. #97 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772428 | 2 |
| #23768371 | 2 |
| #23762023 | 2 |
| #23761740 | 2 |
| #23761256 | 2 |
| C79×#1285 | 2 |
| #9447 | 79 |