Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
462 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 151 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 |
|---|---|---|
| 1. #23776553 | C2 | semidirect |
| 2. #23776541 | C2 | semidirect |
| 3. #23765720 | C2 | semidirect |
| 4. #23765715 | C2 | semidirect |
| 5. #23765709 | C2 | semidirect |
| 6. C2×#19098402 | C2 | semidirect |
| 7. C79×#2258 | C2 | semidirect |
| 13. #19098995 | C22 | semidirect |
| 14. C2×Dic632 | C22 | semidirect |
| 16. Dic1264 | C22 | semidirect |
| 17. #19098402 | C22 | semidirect |
| 18. #19098402 | C22 | semidirect |
| 19. #19098402 | C22 | semidirect |
| 20. D2528 | C22 | semidirect |
| 22. M64×C79 | C22 | semidirect |
| 23. C2×C32×C79 | C22 | semidirect |
| 102. #2258 | D79 | semidirect |
| 103. C79 | #33983 | semidirect |
| 118. M64 | C2×D79 | semidirect |
| 119. C2×C32 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776553 | 2 |
| #23776541 | 2 |
| #23765720 | 2 |
| #23765715 | 2 |
| #23765709 | 2 |
| C2×#19098402 | 2 |
| C79×#2258 | 2 |
| #33983 | 79 |