Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
728 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 163 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. #23774119 | C2 | semidirect |
| 3. #23773796 | C2 | semidirect |
| 4. #23763054 | C2 | semidirect |
| 5. #23763048 | C2 | semidirect |
| 6. #23763042 | C2 | semidirect |
| 7. #23763013 | C2 | semidirect |
| 8. #23761703 | C2 | semidirect |
| 9. C79×#3139 | C2 | semidirect |
| 162. #3139 | D79 | semidirect |
| 168. C79 | #19754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774138 | 2 |
| #23774119 | 2 |
| #23773796 | 2 |
| #23763054 | 2 |
| #23763048 | 2 |
| #23763042 | 2 |
| #23763013 | 2 |
| #23761703 | 2 |
| C79×#3139 | 2 |
| #19754 | 79 |