Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
568 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 83 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. #23763131 | C2 | semidirect |
| 3. #23761711 | C2 | semidirect |
| 4. #23761398 | C2 | semidirect |
| 5. #23761397 | C2 | semidirect |
| 6. #23761396 | C2 | semidirect |
| 7. C79×#1343 | C2 | semidirect |
| 8. C2×#14579157 | C4 | semidirect |
| 13. #19098481 | C4 | semidirect |
| 15. #19098477 | C4 | semidirect |
| 19. #19098427 | C4 | semidirect |
| 242. #1343 | D79 | semidirect |
| 243. C79 | #11693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23769149 | 2 |
| #23763131 | 2 |
| #23761711 | 2 |
| #23761398 | 2 |
| #23761397 | 2 |
| #23761396 | 2 |
| C79×#1343 | 2 |
| #11693 | 79 |