Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
728 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 2. #23765054 | C2 | semidirect |
| 3. #23763953 | C2 | semidirect |
| 17. #563×C79 | C4 | semidirect |
| 18. #559×C79 | C4 | semidirect |
| 197. C79 | #12771 | semidirect |
| 200. #563 | Dic79 | semidirect |
| 201. #559 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765085 | 2 |
| #23765054 | 2 |
| #23763953 | 2 |
| #23763784 | 2 |
| C79×#3550 | 2 |
| #12771 | 79 |