Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
504 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 504 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. #23772456 | C2 | semidirect |
| 3. C2×#19098296 | C2 | semidirect |
| 4. #23761761 | C2 | semidirect |
| 5. #23761287 | C2 | semidirect |
| 6. #23761243 | C2 | semidirect |
| 7. C79×#1504 | C2 | semidirect |
| 9. #19098896 | C4 | semidirect |
| 11. #19098879 | C4 | semidirect |
| 14. #19098713 | C4 | semidirect |
| 16. #19098696 | C4 | semidirect |
| 248. #1504 | D79 | semidirect |
| 253. C79 | #9264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774161 | 2 |
| #23772456 | 2 |
| C2×#19098296 | 2 |
| #23761761 | 2 |
| #23761287 | 2 |
| #23761243 | 2 |
| C79×#1504 | 2 |
| #9264 | 79 |