Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
798 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 798 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. #23773962 | C2 | semidirect |
| 2. #23773961 | C2 | semidirect |
| 3. #23773909 | C2 | semidirect |
| 5. #23763031 | C2 | semidirect |
| 6. #23763029 | C2 | semidirect |
| 7. #23763028 | C2 | semidirect |
| 8. #23763025 | C2 | semidirect |
| 9. #23763024 | C2 | semidirect |
| 10. #322×D79 | C2 | semidirect |
| 11. C79×#1716 | C2 | semidirect |
| 109. C8×D79 | SD16 | semidirect |
| 186. #1716 | D79 | semidirect |
| 192. C79 | #19608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773962 | 2 |
| #23773961 | 2 |
| #23773909 | 2 |
| #23773829 | 2 |
| #23763031 | 2 |
| #23763029 | 2 |
| #23763028 | 2 |
| #23763025 | 2 |
| #23763024 | 2 |
| #322×D79 | 2 |
| C79×#1716 | 2 |
| #19608 | 79 |