Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
556 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 109 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. #23763491 | C2 | semidirect |
| 4. #23763488 | C2 | semidirect |
| 6. #23761267 | C2 | semidirect |
| 7. C79×#1289 | C2 | semidirect |
| 16. #19098503 | C4 | semidirect |
| 17. #19098500 | C4 | semidirect |
| 230. #1289 | D79 | semidirect |
| 231. C79 | #9473 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772426 | 2 |
| #23767718 | 2 |
| #23763491 | 2 |
| #23763488 | 2 |
| #23763385 | 2 |
| #23761267 | 2 |
| C79×#1289 | 2 |
| #9473 | 79 |