Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
784 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 111 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. #23772429 | C2 | semidirect |
| 2. #23763344 | C2 | semidirect |
| 3. C4×#14579076 | C2 | semidirect |
| 4. #23761286 | C2 | semidirect |
| 17. #395×C79 | C4 | semidirect |
| 19. #394×C79 | C4 | semidirect |
| 20. #393×C79 | C4 | semidirect |
| 22. #392×C79 | C4 | semidirect |
| 25. C2×#11929608 | D4 | semidirect |
| 138. C23×C79 | #104 | semidirect |
| 225. C79 | #9009 | semidirect |
| 235. #395 | Dic79 | semidirect |
| 237. #394 | Dic79 | semidirect |
| 238. #393 | Dic79 | semidirect |
| 240. #392 | Dic79 | semidirect |
| 358. C23 | #14579088 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772429 | 2 |
| #23763344 | 2 |
| C4×#14579076 | 2 |
| #23761286 | 2 |
| C79×#2388 | 2 |
| #9009 | 79 |