Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
434 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 434 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. #23763446 | C2 | semidirect |
| 4. #23761530 | C2 | semidirect |
| 5. C79×#1813 | C2 | semidirect |
| 6. C22×C8×D79 | C4 | semidirect |
| 13. #19098591 | C4 | semidirect |
| 16. #19098526 | C4 | semidirect |
| 17. #19098518 | C4 | semidirect |
| 189. #1813 | D79 | semidirect |
| 192. C79 | #12805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772092 | 2 |
| #23765042 | 2 |
| #23763446 | 2 |
| #23761530 | 2 |
| C79×#1813 | 2 |
| #12805 | 79 |