Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
294 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 55 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. #23776533 | C2 | semidirect |
| 2. #23765715 | C2 | semidirect |
| 3. #23765712 | C2 | semidirect |
| 4. #23765504 | C2 | semidirect |
| 5. #23761586 | C2 | semidirect |
| 6. #23761539 | C2 | semidirect |
| 7. C79×#1418 | C2 | semidirect |
| 15. C2×D1264 | C22 | semidirect |
| 22. #19098397 | C22 | semidirect |
| 25. M64×C79 | C22 | semidirect |
| 26. #367×C79 | C22 | semidirect |
| 39. Dic632 | D4 | semidirect |
| 46. D1264 | D4 | semidirect |
| 54. Q32×C79 | D4 | semidirect |
| 56. D16×C79 | D4 | semidirect |
| 150. #1418 | D79 | semidirect |
| 152. C79 | #13667 | semidirect |
| 169. M64 | C2×D79 | semidirect |
| 170. #367 | C2×D79 | semidirect |
| 187. Q32 | D316 | semidirect |
| 196. D16 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776533 | 2 |
| #23765715 | 2 |
| #23765712 | 2 |
| #23765504 | 2 |
| #23761586 | 2 |
| #23761539 | 2 |
| C79×#1418 | 2 |
| #13667 | 79 |