Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
856 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 103 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. #23765085 | C2 | semidirect |
| 3. #23765049 | C2 | semidirect |
| 4. #23763947 | C2 | semidirect |
| 5. C79×#1884 | C2 | semidirect |
| 7. #19099305 | C4 | semidirect |
| 11. #19099198 | C4 | semidirect |
| 16. #19098547 | C22 | semidirect |
| 22. #568×C79 | C22 | semidirect |
| 25. #410×C79 | C22 | semidirect |
| 211. #1884 | D79 | semidirect |
| 212. C79 | #12769 | semidirect |
| 213. #568 | C2×D79 | semidirect |
| 228. #410 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777805 | 2 |
| #23765085 | 2 |
| #23765049 | 2 |
| #23763947 | 2 |
| C79×#1884 | 2 |
| #12769 | 79 |