Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
700 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 700 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. #23766512 | C2 | semidirect |
| 2. C2×#19098360 | C2 | semidirect |
| 3. #23763359 | C2 | semidirect |
| 4. #23761526 | C2 | semidirect |
| 19. #454×C79 | C4 | semidirect |
| 41. 2−1+4×C79 | C2×C4 | semidirect |
| 60. #101×C79 | C2×C4 | semidirect |
| 193. C79 | #13057 | semidirect |
| 198. #454 | Dic79 | semidirect |
| 213. 2−1+4 | C2×Dic79 | semidirect |
| 244. #101 | C2×Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766512 | 2 |
| C2×#19098360 | 2 |
| #23763359 | 2 |
| #23761526 | 2 |
| C2×#454×C79 | 2 |
| #13057 | 79 |