Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
468 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 468 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 |
|---|---|---|
| 2. #23765071 | C2 | semidirect |
| 3. #23765051 | C2 | semidirect |
| 4. #23763446 | C2 | semidirect |
| 5. C79×#1757 | C2 | semidirect |
| 6. C22×D632 | C4 | semidirect |
| 13. #19098601 | C4 | semidirect |
| 14. #19098569 | C4 | semidirect |
| 172. #1757 | D79 | semidirect |
| 173. C79 | #13231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773048 | 2 |
| #23765071 | 2 |
| #23765051 | 2 |
| #23763446 | 2 |
| C79×#1757 | 2 |
| #13231 | 79 |