Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
470 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 131 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. #23776503 | C2 | semidirect |
| 2. #23765136 | C2 | semidirect |
| 3. #23763446 | C2 | semidirect |
| 4. #23761507 | C2 | semidirect |
| 16. #470×C79 | C4 | semidirect |
| 17. #469×C79 | C4 | semidirect |
| 24. #14579101 | D4 | semidirect |
| 144. C79 | #13077 | semidirect |
| 151. #470 | Dic79 | semidirect |
| 152. #469 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776503 | 2 |
| #23765136 | 2 |
| #23763446 | 2 |
| #23761507 | 2 |
| C79×#3060 | 2 |
| #13077 | 79 |