Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1256 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1256 conjugacy classes of subgroups — too many to draw. Only its 183 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. #23774197 | C2 | semidirect |
| 2. #23768880 | C2 | semidirect |
| 3. #23762437 | C2 | semidirect |
| 4. #23762335 | C2 | semidirect |
| 5. #23761916 | C2 | semidirect |
| 6. #23761730 | C2 | semidirect |
| 7. C2×#537×C79 | C2 | semidirect |
| 10. #19098879 | C22 | semidirect |
| 13. #19098696 | C22 | semidirect |
| 15. #19098502 | C22 | semidirect |
| 16. #19098480 | C22 | semidirect |
| 21. #19098297 | C22 | semidirect |
| 22. #19098289 | C22 | semidirect |
| 223. C2×#537 | D79 | semidirect |
| 230. C79 | #18324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774197 | 2 |
| #23768880 | 2 |
| #23762437 | 2 |
| #23762335 | 2 |
| #23761916 | 2 |
| #23761730 | 2 |
| C2×#537×C79 | 2 |
| #18324 | 79 |