Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
716 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 716 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 |
|---|---|---|
| 3. #23761729 | C2 | semidirect |
| 4. #23761309 | C2 | semidirect |
| 231. C79 | #9513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766731 | 2 |
| #23763328 | 2 |
| #23761729 | 2 |
| #23761309 | 2 |
| C79×#2879 | 2 |
| #9513 | 79 |