Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
500 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 71 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. #23763187 | C2 | semidirect |
| 3. #23761715 | C2 | semidirect |
| 4. #23761421 | C2 | semidirect |
| 5. #23761398 | C2 | semidirect |
| 6. #23761396 | C2 | semidirect |
| 7. C79×#1351 | C2 | semidirect |
| 8. C2×#14579150 | C4 | semidirect |
| 13. #19098474 | C4 | semidirect |
| 14. #19098473 | C4 | semidirect |
| 19. #19098430 | C4 | semidirect |
| 225. #1351 | D79 | semidirect |
| 228. C79 | #11730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23769258 | 2 |
| #23763187 | 2 |
| #23761715 | 2 |
| #23761421 | 2 |
| #23761398 | 2 |
| #23761396 | 2 |
| C79×#1351 | 2 |
| #11730 | 79 |