Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
844 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#19098349 | C2 | semidirect |
| 3. #23763392 | C2 | semidirect |
| 4. C4×#99×C79 | C2 | semidirect |
| 5. C23×D316 | C4 | semidirect |
| 13. #19098423 | C4 | semidirect |
| 14. #19098418 | C4 | semidirect |
| 53. #99×C79 | D4 | semidirect |
| 194. C4×C79 | AΣL(1,𝔽16) | semidirect |
| 208. C4×#99 | D79 | semidirect |
| 209. C79 | #13221 | semidirect |
| 257. #99 | D316 | semidirect |
| 400. C4 | #19098349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766756 | 2 |
| C2×#19098349 | 2 |
| #23763392 | 2 |
| C4×#99×C79 | 2 |
| #13221 | 79 |