Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
538 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23763500 | C2 | semidirect |
| 3. #23763475 | C2 | semidirect |
| 5. #23761308 | C2 | semidirect |
| 6. #23761253 | C2 | semidirect |
| 10. #19098879 | C4 | semidirect |
| 11. #19098874 | C4 | semidirect |
| 37. C2×C4⋊Dic79 | C2×C4 | semidirect |
| 38. C2×C4⋊Dic79 | C2×C4 | semidirect |
| 49. C22⋊(C79⋊C8) | C2×C4 | semidirect |
| 239. C79 | #9525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773336 | 2 |
| #23763500 | 2 |
| #23763475 | 2 |
| #23761929 | 2 |
| #23761308 | 2 |
| #23761253 | 2 |
| C79×#2333 | 2 |
| #9525 | 79 |