Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
396 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23765021 | C2 | semidirect |
| 2. #23763446 | C2 | semidirect |
| 3. #23761385 | C2 | semidirect |
| 9. #19098345 | C22 | semidirect |
| 10. #19098320 | C22 | semidirect |
| 11. C22×D8×C79 | C4 | semidirect |
| 14. #469×C79 | C4 | semidirect |
| 18. #427×C79 | C4 | semidirect |
| 155. C79 | #11868 | semidirect |
| 156. C22×D8 | Dic79 | semidirect |
| 160. #469 | Dic79 | semidirect |
| 165. #427 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765021 | 2 |
| #23763446 | 2 |
| #23761385 | 2 |
| C79×#3058 | 2 |
| #11868 | 79 |