Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
502 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 155 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. C22×D1264 | C2 | semidirect |
| 2. #23765712 | C2 | direct (N × H) |
| 3. C2×#19098400 | C2 | semidirect |
| 4. C2×#19098398 | C2 | semidirect |
| 5. C2×#19098397 | C2 | semidirect |
| 6. C2×#508×C79 | C2 | semidirect |
| 11. C2×D1264 | C22 | semidirect |
| 12. #19098400 | C22 | semidirect |
| 13. #19098398 | C22 | semidirect |
| 14. #19098397 | C22 | semidirect |
| 15. C2×C79⋊C32 | C22 | semidirect |
| 18. #508×C79 | C22 | semidirect |
| 19. C2×Q32×C79 | C22 | semidirect |
| 21. C2×D16×C79 | C22 | semidirect |
| 31. C79⋊C32 | C23 | semidirect |
| 40. Q32×C79 | C23 | semidirect |
| 43. D16×C79 | C23 | semidirect |
| 112. C2×C79 | #2263 | semidirect |
| 115. C2×#508 | D79 | semidirect |
| 121. C79 | C2×#2263 | semidirect |
| 125. #508 | C2×D79 | semidirect |
| 126. C2×Q32 | C2×D79 | semidirect |
| 132. C2×D16 | C2×D79 | semidirect |
| 151. Q32 | C22×D79 | semidirect |
| 157. D16 | C22×D79 | semidirect |
| 227. C2 | #23765712 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1264 | 2 |
| #23765712 | 2 |
| C2×#19098400 | 2 |
| C2×#19098398 | 2 |
| C2×#19098397 | 2 |
| C2×#508×C79 | 2 |
| C2×#2263 | 79 |