Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1810 conjugacy classes of subgroups; only the 319 normal subgroups are shown.
This group has 1810 conjugacy classes of subgroups — too many to draw. Only its 319 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. #23761662 | C2 | semidirect |
| 2. #23761649 | C2 | semidirect |
| 3. #23761641 | C2 | semidirect |
| 4. #23761637 | C2 | semidirect |
| 15. #392×C79 | C4 | semidirect |
| 160. C79 | #14651 | semidirect |
| 167. #392 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23761662 | 2 |
| #23761649 | 2 |
| #23761641 | 2 |
| #23761637 | 2 |
| C2×#392×C79 | 2 |
| #14651 | 79 |