Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
412 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23763450 | C2 | semidirect |
| 4. #23761522 | C2 | semidirect |
| 5. C79×#1813 | C2 | semidirect |
| 178. #1813 | D79 | semidirect |
| 180. C79 | #12810 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772116 | 2 |
| #23765083 | 2 |
| #23763450 | 2 |
| #23761522 | 2 |
| C79×#1813 | 2 |
| #12810 | 79 |