Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
906 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 906 conjugacy classes of subgroups — too many to draw. Only its 179 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. #23773980 | C2 | semidirect |
| 2. #23773978 | C2 | semidirect |
| 3. #23773829 | C2 | semidirect |
| 4. #23773823 | C2 | semidirect |
| 5. #23763072 | C2 | semidirect |
| 6. #23763070 | C2 | semidirect |
| 7. #23763068 | C2 | semidirect |
| 8. #23763066 | C2 | semidirect |
| 9. #23763064 | C2 | semidirect |
| 10. #322×D79 | C2 | semidirect |
| 11. C79×#1722 | C2 | semidirect |
| 116. C8×D79 | D8 | semidirect |
| 199. #1722 | D79 | semidirect |
| 204. C79 | #19616 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773980 | 2 |
| #23773978 | 2 |
| #23773829 | 2 |
| #23773823 | 2 |
| #23763072 | 2 |
| #23763070 | 2 |
| #23763068 | 2 |
| #23763066 | 2 |
| #23763064 | 2 |
| #322×D79 | 2 |
| C79×#1722 | 2 |
| #19616 | 79 |