Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1450 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1450 conjugacy classes of subgroups — too many to draw. Only its 191 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. #23777164 | C2 | semidirect |
| 2. #23774318 | C2 | semidirect |
| 3. #23762317 | C2 | semidirect |
| 4. #23761894 | C2 | semidirect |
| 5. #23761721 | C2 | semidirect |
| 6. C79×#2541 | C2 | semidirect |
| 18. #19098697 | C22 | semidirect |
| 19. #19098616 | C22 | semidirect |
| 20. #19098296 | C22 | semidirect |
| 21. #19098287 | C22 | semidirect |
| 23. C2×#127×C79 | C22 | semidirect |
| 26. #392×C79 | C22 | semidirect |
| 28. C4×C4⋊C4×C79 | C22 | semidirect |
| 37. #14579161 | D4 | semidirect |
| 38. #14579158 | D4 | semidirect |
| 50. C4×D316 | D4 | semidirect |
| 116. C2×D4×C79 | D8 | semidirect |
| 217. #2541 | D79 | semidirect |
| 221. C79 | #18387 | semidirect |
| 230. C2×#127 | C2×D79 | semidirect |
| 239. #392 | C2×D79 | semidirect |
| 241. C4×C4⋊C4 | C2×D79 | semidirect |
| 321. C2×D4 | #11929609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777164 | 2 |
| #23774318 | 2 |
| #23762317 | 2 |
| #23761894 | 2 |
| #23761721 | 2 |
| C79×#2541 | 2 |
| #18387 | 79 |