Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
480 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 113 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. #23766149 | C2 | semidirect |
| 5. #23761260 | C2 | semidirect |
| 6. #23761228 | C2 | semidirect |
| 7. C79×#1549 | C2 | semidirect |
| 9. #19098959 | C4 | semidirect |
| 10. #19098911 | C4 | semidirect |
| 185. #1549 | D79 | semidirect |
| 189. C79 | #9302 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774528 | 2 |
| #23766149 | 2 |
| #23764231 | 2 |
| #23761961 | 2 |
| #23761260 | 2 |
| #23761228 | 2 |
| C79×#1549 | 2 |
| #9302 | 79 |