Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
566 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 566 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. #23766691 | C2 | semidirect |
| 5. #23761828 | C2 | semidirect |
| 6. #23761228 | C2 | semidirect |
| 7. C79×#1487 | C2 | semidirect |
| 113. C4×Dic79 | SD16 | semidirect |
| 210. #1487 | D79 | semidirect |
| 212. C79 | #10014 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773432 | 2 |
| #23773431 | 2 |
| #23766691 | 2 |
| #23764231 | 2 |
| #23761828 | 2 |
| #23761228 | 2 |
| C79×#1487 | 2 |
| #10014 | 79 |