Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
452 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 87 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. #23765075 | C2 | semidirect |
| 5. #23763444 | C2 | semidirect |
| 6. #23763203 | C2 | semidirect |
| 7. C79×#2123 | C2 | semidirect |
| 8. C22×#11929611 | C4 | semidirect |
| 16. #19098599 | C4 | semidirect |
| 17. #19098572 | C4 | semidirect |
| 18. #19098567 | C4 | semidirect |
| 216. #2123 | D79 | semidirect |
| 220. C79 | #13229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773041 | 2 |
| #23765075 | 2 |
| #23765071 | 2 |
| #23765051 | 2 |
| #23763444 | 2 |
| #23763203 | 2 |
| C79×#2123 | 2 |
| #13229 | 79 |