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. #23763804 | C2 | semidirect |
| 4. #23763801 | C2 | semidirect |
| 5. #23763617 | C2 | semidirect |
| 6. #23761526 | C2 | semidirect |
| 7. C2×#355×C79 | C2 | semidirect |
| 77. #101×C79 | D4 | semidirect |
| 240. C2×#355 | D79 | semidirect |
| 245. C79 | #13426 | semidirect |
| 312. #101 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23770424 | 2 |
| C2×#19098359 | 2 |
| #23763804 | 2 |
| #23763801 | 2 |
| #23763617 | 2 |
| #23761526 | 2 |
| C2×#355×C79 | 2 |
| #13426 | 79 |