Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
784 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 784 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. #23763343 | C2 | semidirect |
| 3. C4×#14579076 | C2 | semidirect |
| 4. #23761285 | C2 | semidirect |
| 5. C79×#2973 | C2 | semidirect |
| 10. #19098483 | C4 | semidirect |
| 11. #19098480 | C4 | semidirect |
| 13. #19098475 | C4 | semidirect |
| 14. #19098472 | C4 | semidirect |
| 53. C2×M16×C79 | D4 | semidirect |
| 131. C23×C79 | #104 | semidirect |
| 220. #2973 | D79 | semidirect |
| 225. C79 | #9009 | semidirect |
| 256. C2×M16 | C22⋊D79 | semidirect |
| 358. C23 | #14579087 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766615 | 2 |
| #23763343 | 2 |
| C4×#14579076 | 2 |
| #23761285 | 2 |
| C79×#2973 | 2 |
| #9009 | 79 |