Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
542 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 103 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. #23763499 | C2 | semidirect |
| 5. #23761306 | C2 | semidirect |
| 6. #23761286 | C2 | semidirect |
| 7. C79×#2346 | C2 | semidirect |
| 12. #19098606 | C4 | semidirect |
| 13. #19098567 | C4 | semidirect |
| 204. #2346 | D79 | semidirect |
| 210. C79 | #9367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773340 | 2 |
| #23764235 | 2 |
| #23763499 | 2 |
| #23761915 | 2 |
| #23761306 | 2 |
| #23761286 | 2 |
| C79×#2346 | 2 |
| #9367 | 79 |