Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
764 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 81 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. #23772660 | C2 | semidirect |
| 2. #23771428 | C2 | semidirect |
| 3. #23763318 | C2 | semidirect |
| 4. #23761934 | C2 | semidirect |
| 5. #23761929 | C2 | semidirect |
| 6. #23761309 | C2 | semidirect |
| 263. C79 | #9981 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772660 | 2 |
| #23771428 | 2 |
| #23763318 | 2 |
| #23761934 | 2 |
| #23761929 | 2 |
| #23761309 | 2 |
| C79×#3006 | 2 |
| #9981 | 79 |