Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
582 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 582 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. #23763388 | C2 | semidirect |
| 2. #23761738 | C2 | semidirect |
| 3. #23761424 | C2 | semidirect |
| 4. #23761397 | C2 | semidirect |
| 14. C2×C4×D4×C79 | C4 | semidirect |
| 17. #399×C79 | C4 | semidirect |
| 20. #392×C79 | C4 | semidirect |
| 22. #376×C79 | C4 | semidirect |
| 219. C79 | #11821 | semidirect |
| 222. C2×C4×D4 | Dic79 | semidirect |
| 227. #399 | Dic79 | semidirect |
| 230. #392 | Dic79 | semidirect |
| 233. #376 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763388 | 2 |
| #23761738 | 2 |
| #23761424 | 2 |
| #23761397 | 2 |
| C79×#2397 | 2 |
| #11821 | 79 |