Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
512 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 75 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×#19098359 | C2 | semidirect |
| 3. #23763803 | C2 | semidirect |
| 4. #23761527 | C2 | semidirect |
| 5. C79×#1857 | C2 | semidirect |
| 50. #101×C79 | D4 | semidirect |
| 162. #1857 | D79 | semidirect |
| 164. C79 | #13426 | semidirect |
| 208. #101 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23770426 | 2 |
| C2×#19098359 | 2 |
| #23763803 | 2 |
| #23761527 | 2 |
| C79×#1857 | 2 |
| #13426 | 79 |