Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
594 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 4. #23762085 | C2 | semidirect |
| 5. #23761302 | C2 | semidirect |
| 6. #23761301 | C2 | semidirect |
| 7. C79×#1549 | C2 | semidirect |
| 177. #1549 | D79 | semidirect |
| 180. C79 | #9395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772423 | 2 |
| #23768354 | 2 |
| #23763389 | 2 |
| #23762085 | 2 |
| #23761302 | 2 |
| #23761301 | 2 |
| C79×#1549 | 2 |
| #9395 | 79 |