Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
590 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 151 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 |
|---|---|---|
| 1. #23773913 | C2 | semidirect |
| 3. #23765645 | C2 | semidirect |
| 4. #23765643 | C2 | semidirect |
| 5. #23765642 | C2 | semidirect |
| 6. #23765638 | C2 | semidirect |
| 7. #23765106 | C2 | semidirect |
| 8. #346×D79 | C2 | semidirect |
| 9. C79×#2245 | C2 | semidirect |
| 152. #2245 | D79 | semidirect |
| 158. C79 | #33701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773913 | 2 |
| #23773829 | 2 |
| #23765645 | 2 |
| #23765643 | 2 |
| #23765642 | 2 |
| #23765638 | 2 |
| #23765106 | 2 |
| #346×D79 | 2 |
| C79×#2245 | 2 |
| #33701 | 79 |