Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
372 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 372 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 |
|---|---|---|
| 2. #23763537 | C2 | semidirect |
| 5. #23761291 | C2 | semidirect |
| 6. #23761236 | C2 | semidirect |
| 7. C79×#1574 | C2 | semidirect |
| 169. #1574 | D79 | semidirect |
| 174. C79 | #8901 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772529 | 2 |
| #23763537 | 2 |
| #23761837 | 2 |
| #23761780 | 2 |
| #23761291 | 2 |
| #23761236 | 2 |
| C79×#1574 | 2 |
| #8901 | 79 |