Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
512 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 131 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. #23765617 | C2 | semidirect |
| 3. #23765573 | C2 | semidirect |
| 4. #23765478 | C2 | semidirect |
| 6. #23765289 | C2 | semidirect |
| 7. #23765216 | C2 | semidirect |
| 8. C79×#3177 | C2 | semidirect |
| 18. #19098385 | C22 | semidirect |
| 19. #19098384 | C22 | semidirect |
| 20. #19098379 | C22 | semidirect |
| 23. #19098341 | C22 | semidirect |
| 25. #499×C79 | C22 | semidirect |
| 26. #494×C79 | C22 | semidirect |
| 30. #441×C79 | C22 | semidirect |
| 161. #3177 | D79 | semidirect |
| 169. C79 | #33693 | semidirect |
| 174. #499 | C2×D79 | semidirect |
| 175. #494 | C2×D79 | semidirect |
| 183. #441 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772304 | 2 |
| #23765617 | 2 |
| #23765573 | 2 |
| #23765478 | 2 |
| #23765350 | 2 |
| #23765289 | 2 |
| #23765216 | 2 |
| C79×#3177 | 2 |
| #33693 | 79 |