Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
488 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23764390 | C2 | semidirect |
| 5. #23761821 | C2 | semidirect |
| 6. #23761290 | C2 | semidirect |
| 7. C79×#3139 | C2 | semidirect |
| 180. #3139 | D79 | semidirect |
| 185. C79 | #10114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774783 | 2 |
| #23774325 | 2 |
| #23764390 | 2 |
| #23761991 | 2 |
| #23761821 | 2 |
| #23761290 | 2 |
| C79×#3139 | 2 |
| #10114 | 79 |