Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
468 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 103 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. #23765072 | C2 | semidirect |
| 2. #23765050 | C2 | semidirect |
| 3. #23763446 | C2 | semidirect |
| 4. #23763200 | C2 | semidirect |
| 15. C22×D8×C79 | C4 | semidirect |
| 22. #427×C79 | C4 | semidirect |
| 23. #418×C79 | C4 | semidirect |
| 173. C79 | #13231 | semidirect |
| 174. C22×D8 | Dic79 | semidirect |
| 182. #427 | Dic79 | semidirect |
| 183. #418 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765072 | 2 |
| #23765050 | 2 |
| #23763446 | 2 |
| #23763200 | 2 |
| C79×#3058 | 2 |
| #13231 | 79 |