Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
838 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 838 conjugacy classes of subgroups — too many to draw. Only its 107 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. #23765998 | C2 | semidirect |
| 2. #23763344 | C2 | semidirect |
| 3. #23761727 | C2 | semidirect |
| 4. #23761252 | C2 | semidirect |
| 16. #393×C79 | C4 | semidirect |
| 17. #392×C79 | C4 | semidirect |
| 26. C2×C4×Dic79 | D4 | semidirect |
| 198. C79 | #9479 | semidirect |
| 204. #393 | Dic79 | semidirect |
| 205. #392 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765998 | 2 |
| #23763344 | 2 |
| #23761727 | 2 |
| #23761252 | 2 |
| C79×#2404 | 2 |
| #9479 | 79 |