Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
648 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 648 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. #23764382 | C2 | semidirect |
| 2. #23762065 | C2 | semidirect |
| 3. #23761886 | C2 | semidirect |
| 4. #23761865 | C2 | semidirect |
| 15. #564×C79 | C4 | semidirect |
| 18. #563×C79 | C4 | semidirect |
| 20. #562×C79 | C4 | semidirect |
| 184. C79 | #8505 | semidirect |
| 185. #564 | Dic79 | semidirect |
| 188. #563 | Dic79 | semidirect |
| 190. #562 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764382 | 2 |
| #23762065 | 2 |
| #23761886 | 2 |
| #23761865 | 2 |
| C79×#3531 | 2 |
| #8505 | 79 |