Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
334 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 334 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 |
|---|---|---|
| 2. #23764999 | C2 | semidirect |
| 4. #23764186 | C2 | semidirect |
| 5. #23761509 | C2 | semidirect |
| 6. #23761493 | C2 | semidirect |
| 23. #361×C79 | C4 | semidirect |
| 152. C79 | #13144 | semidirect |
| 163. #361 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098364 | 2 |
| #23764999 | 2 |
| #23764311 | 2 |
| #23764186 | 2 |
| #23761509 | 2 |
| #23761493 | 2 |
| C2×#361×C79 | 2 |
| #13144 | 79 |