Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
434 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. #23763448 | C2 | semidirect |
| 4. #23763444 | C2 | semidirect |
| 5. #23761530 | C2 | semidirect |
| 6. #23761528 | C2 | semidirect |
| 9. C23×C79⋊C8 | C4 | semidirect |
| 16. #19098590 | C4 | semidirect |
| 20. #19098527 | C4 | semidirect |
| 21. #19098519 | C4 | semidirect |
| 215. C79 | #12805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772095 | 2 |
| #23765041 | 2 |
| #23763448 | 2 |
| #23763444 | 2 |
| #23761530 | 2 |
| #23761528 | 2 |
| C79×#2120 | 2 |
| #12805 | 79 |